Category theory (2022-23): Lecture 10 (Part 1)

Example categories: groups. complete semilattices and compact Hausdorff spaces. Powersets are free semilattices. Freyd's adjoint functor theorem.

[aaronrobertcattell]

As a first approximation, one could say that category theory is the mathematical study of (abstract) algebras of functions.
Just as group theory is the abstraction of the idea of a system of permutations of a set or symmetries of a geometric object, so category theory arises
from the idea of a system of functions among some objects.

[aaronrobertcattell]

1950’s A. Grothendieck et al. were using category theory with great success
in algebraic geometry.

[aaronrobertcattell]

any two distinct points there exist neighbourhoods of each which are disjoint from each other.