Archives pour la catégorie Mathesis universalis

Bart Jacobs : categorical Logic and Type theory

https://people.mpi-sws.org/~dreyer/courses/catlogic/jacobs.pdf

Publicités

Iconicity and abduction

https://books.google.fr/books?id=Iu4QDQAAQBAJ&pg=PA169&lpg=PA169&dq=allegory+homotopy+type+theory&source=bl&ots=3SWXxTBwqB&sig=i8K4173iDyVVQFmXugXuNfVFJ3Y&hl=fr&sa=X&ved=0ahUKEwixgIi428PXAhWBfFAKHbFzAbU4ChDoAQg-MAk#v=onepage&q=allegory%20homotopy%20type%20theory&f=false

Freyd, Scedrov : categories, allegories

https://books.google.fr/books?id=fCSJRegkKdoC&pg=PR4&lpg=PR4&dq=freyd+scedrov+categories+allegories&source=bl&ots=HDQDTeHg9e&sig=Dc189tOztUJUvg2Y8CX6VEGywC8&hl=fr&sa=X&ved=0ahUKEwiipoLs17PXAhXQ-6QKHROoAFoQ6AEINzAJ#v=onepage&q=freyd%20scedrov%20categories%20allegories&f=false

https://ncatlab.org/nlab/show/Categories%2C+Allegories

https://ncatlab.org/nlab/show/allegory

∞-cosmos : articles

http://nyjm.albany.edu/j/2017/23-35v.pdf

https://www.emis.de/journals/TAC/volumes/32/31/32-31.pdf

https://msp.org/agt/2017/17-1/p08.xhtml

Categories, What’s the Point?

Math ∩ Programming

Perhaps primarily due to the prominence of monads in the Haskell programming language, programmers are often curious about category theory. Proponents of Haskell and other functional languages can put category-theoretic concepts on a pedestal or in a mexican restaurant, and their benefits can seem as mysterious as they are magical. For instance, the most common use of a monad in Haskell is to simulate the mutation of immutable data. Others include suspending and backtracking computations, and even untying tangled rope.

Category theory is often mocked (or praised) as the be-all and end-all of mathematical abstraction, and as such (and for other reasons I’ve explored on this blog) many have found it difficult to digest and impossible to master. However, in truth category theory arose from a need for organizing mathematical ideas based on their shared structure. In this post, I want to give a brief overview of what purpose…

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