10
votes
0answers
277 views

What is the history of the notion of subdivision of categories?

A recent answer by Peter May prompts me to ask a question which I have been considering to ask for several months. (The reason why I have not asked it before is that it is not directly related to my ...
7
votes
2answers
547 views

Historical Question about Simplicial Sets

I have a pretty easy historical question about simplicial sets. Unless I am mistaken, simplicial sets first came out of topology, explicitly from combinatorial topology and the study of simplicial ...
11
votes
7answers
2k views

History of classifying spaces

Where did the idea and formal definition of the "classifying space of a (small) category" first appear? Added: As Andy Putman noted below, the "classical" early reference for this is G. Segal's ...
6
votes
0answers
447 views

Historical and terminological questions about Dan Kan's Ex functor and its relation to the classical case of simplicial complexes

Recall that we may define a functor $\xi:\Delta\to \operatorname{Poset}$ sending a simplex $[n]$ to the set of monotone injections $[k]\hookrightarrow [n]$ for $k\geq 0$ (effectively, $k\leq n$ as ...