(formal) construction: intro to category theory

what is a category?

dots and arrows

identity

composition

associativity

what emerges from this structure?

diagrams commute

isomorphism

universal properties

terminal, initial objects

“bestness” and uniqueness

limits, products

enriched categories

morphisms with structure

$\infty$-categories

morphisms between morphisms (and beyond)

(can anyone see the punchline?)

categories of categories

Cat: a category whose objects are categories

functors

maps between categories

morphisms in Cat

natural transformations

morphisms between functors

“translations between translations”