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Category Theory

This is a self study course (module) in category theory which aims to follow the introduction and presentation of category theory found David Spivak's Category Theory for the Sciences.

In particular, the course is aimed at introducing enough mechanics from abstract algebra and other disciplines so that one can enjoy a relatively self-contained first forray into the subject. Spivak's text seemed to do this better than most, and it is for this reason that it was chosen as the backbone of this module. Spivak provides motivating examples which make concrete the exceedingly abstract concepts to be found in category theory. This is in part due to his use of ontological logs (Ologs) to describe relations between things (arrows between objects and English readings of such diagrams). This is a unique (maybe controversial) way of representing knowledge that has been espoused by Spivak since 2010.

Materials collected for self-study of category theory are available to those who have been given access. Full PDFs of current textbooks cannot be widely distributed for free, as a result of © laws.

See the wiki for reading guides, notes, and other information related to self-study of category theory.

How to use this repository

Read the wiki.

This repository is designed to provide a point of reference for controlled-access materials (a private GitHub repository) as well as a wiki fleshed out by either an instructor, or one or more authors who are actively engaged with learning the material (like me).

If this respository were to be used in a class setting, individual students could fork the repo and then use GitHub Projects to manage ongoing questions, problem areas, bookmarks, or whatever. Furthermore, a forked repository allows students to host their own notes and begin assembling their own version of a course. These versions are relatively easy to make use of should an instructor wish to augment his or her own notes, solutions, materials, etc.

Why GitHub? GitHub seems relatively future proof: one can download entire repositories of materials, their wikis, and make changes both through GitHub and on local machines. At the end of the day, one has a website that can be reduced to text files and moved around without worrying about proprietary software and ecosystems. It's all text (and PDFs, and images) and hyperlinks.

Oh, and it's version controlled, because everything is backed by Git. There is a history of a course's evolution, and that history should evolve through collaboration among instructors and students. GitHub is nice for that.


A self study course in Category which follows Spivak, supplemented with other resources.







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