Comment on Anybody?
kogasa@programming.dev 1 week ago🍕(–, B) : C -> Set denotes the contravariant hom functor, normally written Hom(–, B).
In this case, C is a category, and B is a fixed object in that category. For any given object X in C, the hom-set Hom(X, C) is the set of morphisms X -> B in C. For a morphism f : X -> Y in C, the Set morphism Hom(f, B) : Hom(Y, B) -> Hom(X, B) is defined by sending each g : Y -> B to gf : X -> B. This is the mapping C -> Set defined by Hom(–, C), and it’s a (contravariant) functor because it respects composition: if h : X -> Y and f : Y -> Z then fh : X -> Z and Hom(fh, C) = Hom(h, C)Hom(f, C) sends g : Z -> B to gfh.
gerryflap@feddit.nl 1 week ago
Okay I have some reading to do haha. Thanks for the explanation!
As a programmer (who also did quite some math) it never ceases to amaze me how often math just uses single character variable/function names that apparently have a specific meaning. For instance the P^(n)® thingy. Without knowing this specific notation, one might easily assume it meant something else like power sets. Even within the niche I’m more familiar with (machine learning) there was plenty of that stuff going around.
Then again, this meme has an incentive to make it harder, it wouldn’t be funny if it explained symbols.
kogasa@programming.dev 1 week ago
Math builds up so much context that it’s hard to avoid the use of shorthand and reused names for things. Every math book and paper will start with definitions. So it’s not really on you for not recognizing it here