This document is part of my notes on my category theory senior project under Dr. Robert Easton. The document is written in org hosted on github here.
Following a basic introduction to category theory, I’m interested in studying some advanced topic, which topic yet, I don’t know. I’m interested in Algebraic Geometry, sheafs, schemes, topoi, stacks etc. I’m also interested in ∞-Catgeories. And perfectoid spaces, but those are mostly unrelated, though I haven’t seen a category theoretic perspective on them.
- Version Space Algebras. The basic VSA paper I presented.
- What is an ∞-Category A what is article by Lurie. I should read through and take notes on this one.
This is sort of ordered by interest, but losely
- The n-Category Cafe Where all the cool math people hangout
- nLab The best and most consistent online resource I’ve found for higher category theory. Somewhat unreadable.
- Math3ma Generally a very readable version of category theoretic concepts
- Representable Functors from a CS point of view
- Leinster Tom Leinster has a book on basic category theory which is good, and a book on higher category theory I haven’t touched.
- The Stacks project A open source textbook for the theory of stacks
- The Kerodon project Ran by Lurie, higher homotopy version of the stacks project.
- Arrow categories vs Set categories? What are the meaningful differences here? When will I need to define which I am working in? Small and large categories still apply here, correct?
- Are arrow only categories interesting? Is this the start of the perspective I should be thinking in?
- Can a functor from a category to itself be regarded as a subset of the morphisms on that category? I’m thinking of the power set functor, where you don’t need to realize the functor definiton to consider the power set.
- What about self functors? When is a general morphism a functor. Like the commutator vs center map. Is there a general way to tell when you have a functor?
- How does using a Universe or Class get around the same large/small problem with Cat? I should be able to answer this based on the textbook.
- Cat is the category of small categories. The problem still arrises when considering the category of classes etc.
- What is the use of arrow only categories? Are they related to yoneda and hom functors?