QC

Just made me think: "Category theory" is an absolutely terrible name for Category theory. What would you call it if you could rename it?

categories are such absurdly general objects that they need to have multiple names for use in different contexts, modeling different things. we already have terminology like this, e.g. sometimes we call a functor F : J -> C a “diagram of shape J in C”

“category” activates a particular context involving what one might call “big” categories of mathematical objects, e.g. groups, rings, topological spaces. working with “little” categories such as BG for a group G feels quite different - “categories *as* mathematical objects”

the big / little boundary isn’t sharp and there are examples that straddle it like the poset of subobjects of a given object. “web” might not be a bad name for categories that specifically evokes the “little” context, i like “category” fine for the “big” context