/sci/ - Science & Math

>>15014031
>Everything's just a functor?
To the extent that categories are a general context for associative operations and functors are homomorphisms of such contexts, it shouldn't be too surprising that it pops up.

Functors in topology (I mean sheaf theory) just code continuous function spaces effectively.
But not everything is associative, and so you cane come up with even algebraic things where the native formulation usually doesn't smell too much of category theory (at least if you restrict yourself to sane diagrams). The commutator C=[A,B] as a map of (A,B) being such a non-associative thing.
Here's another, much smaller one: The function which takes two rock-paper-scissors players A,B who have chosen as move, and returns the winner C of the game.

PS the nLab doesn't contain the finite sum formula, time to REEE