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ComputationalTrinitarianism.md

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* An Introduction to n-Categories - John C. Baez [(arXiv)](https://arxiv.org/abs/q-alg/9705009)
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* Basic Bicategories - Tom Leinster [(arXiv)](https://arxiv.org/abs/math/9810017)
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* The periodic table of n-categories - Eugenia Cheng [(video)](https://www.youtube.com/watch?v=lJGUMlgCxz8)
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* Monoidal Categories, Higher Categories - Jamie Vicary [(course notes)](http://events.cs.bham.ac.uk/mgs2019/vicary.pdf)
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* Associative n-categories - Christoph Dorn [(arXiv:1812.10586)](https://arxiv.org/pdf/1812.10586.pdf)
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* Strictly associative and unital higher category theory - Jamie Vicary [(slides)](https://www.cs.bham.ac.uk/~axj/files/mgs-xmas-2018-Jamie.pdf)
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* [kerodon.net](https://kerodon.net/) Part I - Higher category theory
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* Category Theory, Toposes - MathProofsable [(video playlist)](https://www.youtube.com/playlist?list=PL4FD0wu2mjWM3ZSxXBj4LRNsNKWZYaT7k)
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* Toposes, Triples and Theories - Michael Barr, Charles Wells [(pdf)](http://www.math.mcgill.ca/barr/papers/tttall.pdf)
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* Topos theoretic background - Olivia Caramello [(paper)](http://www.oliviacaramello.com/Unification/ToposTheoreticPreliminariesOliviaCaramello.pdf)
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* Introduction to categorical logic, classifying toposes and the bridge technique - Olivia Caramello [(videos with toc)](https://sites.google.com/site/logiquecategorique/autres-seminaires/ihes/ihestopos/cours/20151124-caramello)
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* [Topos online 2021](https://aroundtoposes.com/toposesonline/) conference [(videos)](https://www.youtube.com/playlist?list=PLx5f8IelFRgGuSn4L90j3taAGSzyfw-U1)
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* Introduction to categorical logic, classifying toposes and the bridge technique - Olivia Caramello [(videos)](https://www.youtube.com/@IhesFr/search?query=categorical%20logic%2C%20classifying%20toposes)
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* Topos online 2021 conference [(videos)](https://www.youtube.com/playlist?list=PLx5f8IelFRgGuSn4L90j3taAGSzyfw-U1)
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* [Toposes in Como 2018](http://tcsc.lakecomoschool.org/) conference: [(video playlist)](https://www.youtube.com/watch?v=85hAGaFCsD8&index=2&list=PLh_3Q6ZRqWs0LBptMGClJ8OArR0fBT6Pp), [(slides from talks)](http://tcsc.lakecomoschool.org/program/); There are introductory lectures [Some glances at topos theory - Francis Borceux](https://www.youtube.com/watch?v=s_fN9euuVAY&list=PLh_3Q6ZRqWs0LBptMGClJ8OArR0fBT6Pp&index=10)
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* [Topos à l’IHES 2015](https://indico.math.cnrs.fr/event/747/) conference: [(video playlist)](https://www.youtube.com/playlist?list=PLx5f8IelFRgFjhhrWWl96sRSClcG5YIx6), includes introductory: [A crash course in topos theory: the big picture - André Joyal](https://sites.google.com/site/logiquecategorique/autres-seminaires/ihes/ihestopos/cours/joyal)
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* [Topos à l’IHES 2015](https://indico.math.cnrs.fr/event/747/) conference: [(video playlist)](https://www.youtube.com/playlist?list=PLx5f8IelFRgFjhhrWWl96sRSClcG5YIx6), includes introductory: A crash course in topos theory: the big picture by André Joyal
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* Higher Topos Theory - Jacob Lurie [(arXiv:math/0608040)](https://arxiv.org/abs/math/0608040)
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* [Basics in category and topos theory - David Janin](https://www.labri.fr/perso/janin/Enseignement/EDMI/full.html)
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* An Introduction to Topos Theory - Ryszard Paweł Kostecki [(lecture notes)](https://www.fuw.edu.pl/~kostecki/ittt.pdf)
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* Network Models - John C. Baez, John Foley, Joseph Moeller, Blake S. Pollard [(arXiv)](https://arxiv.org/abs/1711.00037)
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* A coalgebraic model of graphs - Christian Jäkel [(arXiv)](https://arxiv.org/abs/1508.02169)
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* Coalgebraic Modelling Applications in Automata Theory and Modal Logic - Helle Hvid Hansen [(pdf)](https://www.cs.vu.nl/en/Images/HH_Hansen_14-05-2009_tcm210-259639.pdf)
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* Compositional game theory reading list - Jules Hedges [(blog post)](https://julesh.com/2017/11/09/compositional-game-theory-reading-list/)
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* A mathematical theory of resources - Bob Coecke, Tobias Fritz, Robert W. Spekkens [arXiv:1409.5531](https://arxiv.org/abs/1409.5531) (application of CT for resource management)
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* The Mathematical Specification of the [Statebox](https://statebox.org/) Language - Statebox Team: Fabrizio Genovese, Jelle Herold [arXiv:1906.07629](https://arxiv.org/abs/1906.07629) (programming language based on CT and petri nets)
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* [Fancy Algebra - Part I: Adjoint Functors](http://www.math.miami.edu/~armstrong/FA/FA_part1.pdf)
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* [varkor/quiver](https://github.com/varkor/quiver)Tooll for drawing commuate diagrams
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## Publications
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This is very opinionated selection of authors that publish interesting papers about `Category Theory`, `Type Theory` and other branches of `Logic`, `Proof Theory`.
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* Haskell Wiki [Functional_pearls](https://wiki.haskell.org/Research_papers/Functional_pearls), [Monads and arrows](https://wiki.haskell.org/Research_papers/Monads_and_arrows)
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* [Samson Abramsky](https://dblp.uni-trier.de/pers/hd/a/Abramsky:Samson)
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* [Benedikt Ahrens](https://dblp.org/pers/hd/a/Ahrens:Benedikt), [personal page](https://benediktahrens.net/publications/)
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* [Thorsten Altenkirch](https://dblp.org/pers/hd/a/Altenkirch:Thorsten), [University of Nottingham page](https://www.cs.nott.ac.uk/~psztxa/publ/)
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* [Nada Amin](https://dblp.org/pers/hd/a/Amin:Nada), [Cambridge University page](https://www.cl.cam.ac.uk/~na482/cv/)
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* [Carlo Angiuli](https://dblp.org/pers/hd/a/Angiuli:Carlo), [Carnegie Mellon University page](https://www.cs.cmu.edu/~cangiuli/), [arxiv](https://arxiv.org/search/cs?query=Carlo+Angiuli&searchtype=author&abstracts=show)
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* [Robert Atkey](https://www.strath.ac.uk/staff/atkeyrobertdr/)
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* [John Baez](https://dblp.uni-trier.de/pers/hd/b/Baez:John_C=), [University of California page](http://math.ucr.edu/home/baez/papers.html)
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* [Michael Barr](http://www.math.mcgill.ca/barr/)
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* [Edwin Brady](https://www.cs.st-andrews.ac.uk/directory/person?id=eb), [personal page](https://edwinb.wordpress.com/publications/)
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* [Olivia Caramello](https://dblp.uni-trier.de/pers/hd/c/Caramello:Olivia), [1](http://www.oliviacaramello.com/Research/Research.htm), [2](http://www.oliviacaramello.com/Papers/Papers.htm), [3](http://www.oliviacaramello.com/Teaching/Teaching.htm)
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* [Eugenia Cheng](http://eugeniacheng.com/math/research/)
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* [J. R. B. Cockett](https://arxiv.org/search/math?searchtype=author&query=Cockett%2C+J+R+B)
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* [Thierry Coquand](https://dblp.uni-trier.de/pers/hd/c/Coquand:Thierry)
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* [Brian Day](http://web.science.mq.edu.au/~street/Day.pub.html), [arXiv](https://arxiv.org/search/math?searchtype=author&query=Day%2C+B+J)
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* [Peter Dybjer](https://dblp.uni-trier.de/pers/hd/d/Dybjer:Peter), [Chalmers University page](http://www.cse.chalmers.se/~peterd/)
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* [Conal Elliott](http://dblp.org/pers/hd/e/Elliott:Conal), [personal page](http://conal.net/papers/)
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* [Martín Hötzel Escardó](https://dblp.uni-trier.de/pers/hd/e/Escard=oacute=:Mart=iacute=n_H=ouml=tzel), [University of Birmingham page](https://www.cs.bham.ac.uk/~mhe/)
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* [Eric Finster](https://dblp.org/pers/hd/f/Finster:Eric), [personal page](http://ericfinster.github.io/)
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* [Brendan Fong](https://dblp.uni-trier.de/pers/hd/f/Fong:Brendan), [personal page](Brendan Fong)
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* [Murdoch James Gabbay](http://www.gabbay.org.uk/), [arxiv](https://arxiv.org/search/cs?searchtype=author&query=Gabbay%2C+M+J)
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* [Fabrizio Genovese](https://www.cs.ox.ac.uk/people/fabrizio.genovese/), [arxiv](https://arxiv.org/search/math?searchtype=author&query=Genovese%2C+F)
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* [Neil Ghani](https://personal.cis.strath.ac.uk/neil.ghani/pub.html)
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* [Jeremy Gibbons](https://dblp.uni-trier.de/pers/hd/g/Gibbons:Jeremy?q=Jeremy%20Gibbons)
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* [Robert Harper](https://dblp.uni-trier.de/pers/hd/h/Harper_0001:Robert), [Carnegie Mellon University](http://www.cs.cmu.edu/~rwh/papers/index.html)
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* [Ralf Hinze](https://dblp.uni-trier.de/pers/hd/h/Hinze:Ralf)
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* [John Hughes](https://www.researchgate.net/profile/John_Hughes13)
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* [Graham Hutton](https://dblp.uni-trier.de/pers/hd/h/Hutton:Graham), [University of Nottingham page](http://www.cs.nott.ac.uk/~pszgmh/#bibliography)
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* [Valery Isaev](https://dblp.uni-trier.de/pers/hd/i/Isaev:Valery), [JET Brains Research page](https://research.jetbrains.org/researchers/valis)
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* [Mauro Jaskelioff](https://dblp.uni-trier.de/pers/hd/j/Jaskelioff:Mauro)
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* [Johan Jeuring](https://dblp.uni-trier.de/pers/hd/j/Jeuring:Johan), [Utrecht University page](http://www.staff.science.uu.nl/~jeuri101/homepage/Publications/index.html)
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* [André Joyal](https://dblp.uni-trier.de/pers/hd/j/Joyal:Andr=eacute=), [arxiv](https://arxiv.org/search/math?query=Andr%C3%A9+Joyal&searchtype=author)
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* [Jacob Lurie](https://www.math.ias.edu/~lurie/)
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* [Jade Master](https://arxiv.org/search/math?searchtype=author&query=Master%2C+J)
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* [Lucius Gregory Meredith](https://dblp.org/pers/hd/m/Meredith:Lucius_Gregory)
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* [David Jaz Myers](http://davidjaz.com/), [arxiv](https://arxiv.org/search/math?searchtype=author&query=Myers%2C+D+J)
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* [Martin Odersky](https://dblp.uni-trier.de/pers/hd/o/Odersky:Martin), [EPFL page](http://lampwww.epfl.ch/~odersky/publications.html)
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* [Craig A. Pastro](https://dblp.uni-trier.de/pers/hd/p/Pastro:Craig_A=), [arXiv](https://arxiv.org/search/math?searchtype=author&query=Pastro%2C+C+A)
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* [Simon Peyton Jones](https://dblp.uni-trier.de/pers/hd/j/Jones:Simon_L=_Peyton), [MS Reasearch page](https://www.microsoft.com/en-us/research/people/simonpj/#!publications)
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* [Oleg Kiselyov](https://dblp.org/pers/hd/k/Kiselyov:Oleg), [personal page](http://okmij.org/ftp/)
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* [Jacob Lurie](https://www.math.ias.edu/~lurie/)
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* [Conor McBride](http://strictlypositive.org/publications.html)
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* [Heather Miller](https://dblp.org/pers/hd/m/Miller:Heather)
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* [Ulf Norell](https://dblp.uni-trier.de/pers/hd/n/Norell:Ulf), [University of Gothenburg page](https://www.gu.se/english/about_the_university/staff/?publicationPageNumber=1&selectedTab=2&languageId=100001&userId=xnoreu)
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* [Russell O'Connor](https://dblp.uni-trier.de/pers/hd/o/O=Connor:Russell)
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* [Emily Riehl](http://www.math.jhu.edu/~eriehl/#research)
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* [Exequiel Rivas](https://dblp.org/pers/hd/r/Rivas:Exequiel)
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* [Peter Selinger](https://dblp.org/pers/hd/s/Selinger:Peter), [Dalhousie University page](https://www.mscs.dal.ca/~selinger/papers.html)
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* [David Spivak](http://math.mit.edu/~dspivak/), [arXiv](https://arxiv.org/search/math?searchtype=author&query=Spivak%2C+D+I)
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* [Jon Sterling](http://www.jonmsterling.com/)
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* [Ross Street](http://web.science.mq.edu.au/~street/Publications.htm), [wikipedia has links to publications](https://en.wikipedia.org/wiki/Ross_Street), [arXiv](https://arxiv.org/search/math?searchtype=author&query=Street%2C+R)
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* [Wouter Swierstra](https://dblp.org/pers/hd/s/Swierstra:Wouter), [Utrecht University page](http://www.staff.science.uu.nl/~swier004/publications/)
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* [Tarmo Uustalu](http://cs.ioc.ee/~tarmo/papers/), [arXiv](https://arxiv.org/search/?query=Tarmo+Uustalu&searchtype=author&source=header)
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* [Christina Vasilakopoulou](https://thalis.math.upatras.gr/~cvasilak/), [arXiv](https://arxiv.org/search/math?searchtype=author&query=Vasilakopoulou%2C+C)
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* [Philip Wadler](https://iohk.io/en/research/library/authors/philip-wadler/), [Monads, arrows, applicatives](http://homepages.inf.ed.ac.uk/wadler/topics/monads.html), [Parametricity](http://homepages.inf.ed.ac.uk/wadler/topics/parametricity.html)
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## [Proof Theory](https://ncatlab.org/nlab/show/proof+theory)
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* DeepSpec Summer School [(2018 videos)](https://deepspec.org/event/dsss18/videos.html) [(2017 video playlist)](https://www.youtube.com/watch?v=jG61w5pOc2A&list=PLovJjGVqXXf3RgVdCXH96pPwSjFLDhSri), based on Software Foundations [(book)](https://softwarefoundations.cis.upenn.edu/)
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* Homotopy Type Theory - Carnegie Mellon University - Robert Harper [(course)](http://www.cs.cmu.edu/~rwh/courses/hott/) lecture notes, papers
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* Computational Higher Type Theory - Carnegie Mellon University - Robert Harper [(course)](http://www.cs.cmu.edu/~rwh/courses/chtt/)
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* Kerodon (book about categorical homotopy theory) [(book)](https://kerodon.net/kerodon.pdf) [(links)](https://kerodon.net/bibliography)
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* Dependent Types in the Idris Programming Language - OPLSS 2017 - Edwin Brady [(slides, examples)](https://www.idris-lang.org/documentation/workshops/oplss-2017-course-materials/) [(video lectures)](https://www.cs.uoregon.edu/research/summerschool/summer17/topics.php)
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* Dependent Types in the Idris Programming Language - OPLSS 2017 - Edwin Brady [(video lectures)](https://www.cs.uoregon.edu/research/summerschool/summer17/topics.php)
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* Advanced Functional Programming (in Agda) - University of Strathclyde - Conor McBride [(github 2017)](https://github.com/pigworker/CS410-17), [(github 2018)](https://github.com/pigworker/CS410-18)
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* [Dependently typed programming in Agda - EUTypes Summer School 2017 - Conor McBride](https://sites.google.com/view/summerschool2017-eutypes/lectures/dependently-typed-programming-in-agda) [(github)](https://github.com/pigworker/Ohrid-Agda)
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* Introduction to programming with dependent types in Scala (2019) - Dmytro Mitin [(course)](https://stepik.org/course/49181/promo), based on library [ProvingGround](http://siddhartha-gadgil.github.io/ProvingGround/) that was used to [solve Polymath 14 problem](https://polymathprojects.org/2018/01/26/spontaneous-polymath-14-a-success/) [resulting](http://math.iisc.ac.in/~gadgil/presentations/HomogeneousLengths.html#/) in [(paper)](https://arxiv.org/abs/1801.03908)
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* On Voevodsky’s Univalence principle - André Joyal [(video, paper)](https://video.ias.edu/VoevodskyMemConf-2018/0911-AndreJoyal) (mathematical foundations behind HoTT and Univalence principle)
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* Introduction to Homotopy Type Theory (Agda) - EUTypes Summer School 2018 - Fredrik Nordvall Forsberg [(slide, exercises src)](https://personal.cis.strath.ac.uk/fredrik.nordvall-forsberg/ohrid-school-hott2018/)
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* Introduction to Dependent Type Theory - EUTypes Summer School 2018 - Matthieu Sozeau [(slides)](https://www.irif.fr/~sozeau/teaching/TYPES18.en.html)
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* Workshop: "Types, Homotopy, Type theory, and Verification" 2018 [(video playlist)](https://www.youtube.com/playlist?list=PLul8LCT3AJqQxIaZhaSNCTuLYfIFB1AiI), [(schedule, abstracts, links to videos)](https://www.him.uni-bonn.de/programs/past-programs/past-trimester-programs/types-sets-constructions/workshop-types-homotopy-type-theory-and-verification/schedule/)
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* FAMOUS - Foundations of Mathematics: Univalent foundations and set theory 2016 [(video playlist)](https://www.youtube.com/watch?v=slVcTtwX_Sk&list=PLQRKUSOIMEh1Arz0-WBgD_Pol4S50HATv), [(videos, slides, abstracts)](http://fomus.weebly.com/talks-abstracts--videos.html)
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* HOTTEST - Homotopy Type Theory Electronic Seminar Talks - 2018 - present [(links to videos)](https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html), [(youtube videos)](https://www.youtube.com/user/jdchristensen123/videos)
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* Introduction to Univalent Foundations of Mathematics with Agda - MGS 2019 - Martín Hötzel Escardó [(lecture notes)](https://www.cs.bham.ac.uk/~mhe/HoTT-UF-in-Agda-Lecture-Notes/index.html) [(github)](https://github.com/martinescardo/HoTT-UF-Agda-Lecture-Notes)
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* Cubical Agda and its extensions, HoTTEST - Andrea Vezzosi [(code)](https://github.com/Saizan/hottest-talk), [(video)](https://www.youtube.com/watch?v=9RFt1Q2pHE8)
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* Cubical Tutorial. Introduction Course - Maxim Sokhatsky [plan and notes of seminar about HoTT and Cubical TT](https://groupoid.space/course/), [more](https://groupoid.space/)Maxim Sokhatsky [plan and notes of seminar about HoTT and Cubical TT](https://groupoid.space/course/), [more](https://groupoid.space/)
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* [groupoid.space](https://groupoid.space/)
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* Cubical Adventures (in Agda) - University of Strathclyde - Conor McBride [(video)](https://www.youtube.com/watch?v=W5-ulP_JzNc)
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* Investigations into cubical type theory - Hugo Herbelin [(video)](https://www.youtube.com/watch?v=zJdwPa_tkSU&list=PLul8LCT3AJqS9FcdKnV4TfiR48Hqcna1I&index=16)
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* Computational Higher Type Theory - Carnegie Mellon University - Robert Harper [(course)](http://www.cs.cmu.edu/~rwh/courses/chtt/)
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* Univalent categories and the Rezk completion - Benedikt Ahrens, Chris Kapulkin, Michael Shulman [(paper)](https://arxiv.org/abs/1303.0584), [(original repository - now merged into UniMath)](https://github.com/benediktahrens/rezk_completion)
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* Displayed Categories - Benedikt Ahrens, Peter LeFanu Lumsdaine [(paper)](https://arxiv.org/abs/1705.04296)
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* Bicategories in Univalent Foundations - Benedikt Ahrens, Dan Frumin, Marco Maggesi, Niels van der Weide [(paper)](https://arxiv.org/abs/1903.01152)
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* [HoTT book - Coq](https://github.com/HoTT/HoTT/tree/master/theories/Categories) described in [HoTT book](https://homotopytypetheory.org/coq/)
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* [HoTT book - Coq](https://github.com/HoTT/HoTT/tree/master/theories/Categories) described in [HoTT book](https://homotopytypetheory.org/book/)
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* (Cubical Agda) Univalent Categories A formalization of category theory in Cubical Agda - Frederik Hanghøj Iversen [(paper)](http://publications.lib.chalmers.se/records/fulltext/256404/256404.pdf), [(fredefox/cat)](https://github.com/fredefox/cat)
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* (Agda) Formalisation of Restriction Categories in Agda [jmchapman/restriction-categories](https://github.com/jmchapman/restriction-categories) for [Introduction to restriction categories - Robin Cockett](http://cs.ioc.ee/~tarmo/tsem12/cockett.html)
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* [jmchapman/categories](https://github.com/jmchapman/categories)

Optics.md

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## Van Laarhoven Optics
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* [Monocle Learning Resources](https://julien-truffaut.github.io/Monocle/learning_resources.html)
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* [Twan van Laarhoven: CPS based functional references](https://www.twanvl.nl/blog/haskell/cps-functional-references)
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* [Functor Optics](http://oleg.fi/gists/posts/2017-12-23-functor-optics.html)
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@@ -90,4 +89,4 @@ trait Grates[S, T, A, B] { // https://r6research.livejournal.com/28050.html
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* Jeremy Gibbons - Profunctor Optics Modular Data Accessors [(video)](https://www.youtube.com/watch?v=sfWzUMViP0M)
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* Grate: A new kind of Optic: [(blog post)](https://r6research.livejournal.com/28050.html)
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* Tambara Modules - Brendan Fong [(video)](https://www.youtube.com/watch?v=67hJW6J4Mic)
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* Profunctor optics, a categorical update - Mario Román, Bryce Clarke, Fosco Loregian, Emily Pillmore, Derek Elkins, Bartosz Milewski [(video)](https://www.youtube.com/watch?v=ceCwD7L0t3w), [(slides)](http://events.cs.bham.ac.uk/syco/strings3-syco5/slides/roman.pdf), [(gist)](https://gist.github.com/emilypi/407838d9c321d5b21ebc1828ad2bedcb)
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* Profunctor optics, a categorical update - Mario Román, Bryce Clarke, Fosco Loregian, Emily Pillmore, Derek Elkins, Bartosz Milewski [(video)](https://www.youtube.com/watch?v=ceCwD7L0t3w), [(gist)](https://gist.github.com/emilypi/407838d9c321d5b21ebc1828ad2bedcb)

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