(formal) construction: intro to category theory
what is a category?
dots and arrows
identity
it is raining -> it is raining
composition
it is raining -> it is cloudy -> earth has clouds
associativity
it is raining -> it is cloudy -> earth has clouds -> earth has an atmosphere
commutative diagram
what emerges from this structure?
isomorphism
it is raining <-> rain is falling from the sky
user ids <-> ssns VS user ids -> first names
universal properties
everything as relational
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”