2025-09-19
This following is a very brief summary of what happened in class on 2025-09-19.
We introduced the notion of a map between categories, called a functor. Each functor consists of two maps: an object map and an arrow map. These two maps must "respect the categorical structure," which basically means they commute with composition and send identity arrows to identity arrows. We then spent the rest of our time looking at a few examples, namely:
- The power set functor
- Some forgetful functors, mainly from "concrete" categories like
to - The abelianization functor
, which we will later see is an adjoint to the forgetful functor
Concepts
References
- Mac Lane, Categories for the Working Mathematician: pp. 13-15