niss

im gay animals irl. it's true

enjoyer of type systems and weird creatures

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sofsh
@sofsh asked:

If you could rename any math concept to anything else of your choosing, what would you rename, and to what?

watch out, ignorant opinions coming in hot!!!

my biggest pet peeve is when a structure is named after the symbol used to write it. ok, no, my biggest pet peeve is when a structure is named after a symbol not used to write it.

so motherfucker number one is the comma category between S and T, which is written.....

ST

what should it be called, though. that is a harder question. it is basically the morphisms starting from somewhere touched by S and ending somewhere touched by T, so, i think maybe "morphism category", but that's already taken, by the thing that is all the morphisms. but that is still a comma category. so, if i'm allowed to rename two things, then comma categories are now morphism categories and the things that were called that are now, uh, total morphism categories maybe?

sorry if this just reads like word salad


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in reply to @niss's post:

God, I have not heard of these before but I fully agree with you. Why are they called that. Thanks for answering my question! Math is so bad at names sometimes that I could tell there had to be an answer.

i can only assume that someone must have written it "S,T" but i have literally never seen it. and it would still be a very undescriptive name even so

edit: uh it says on the wikipedia page i linked that they were originally written like that lol. but they're not any more, by anyone, i don't think

it might be easier to visualise if you think of S and T as kinda selecting subsets of the objects, then S↓T's objects are all the original morphisms that start in the first set and end in the second one. and S↓T's own morphisms are commutative squares between those

maybe that didn't actually help. sorry

yeah, me too. i think it should be some kind of right-pointing Something

and uh, the square thing is kinda like:

  • you start with two objects (of S↓T, so, morphisms), an A→B and an A'→B'
  • you want a way to get to A→B'. with what you currently have, you need either an A→A' or a B→B'
  • since you don't want to make an arbitrary choice about which one, you actually require both, plus a square to make sure they're consistent with each other