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 research and that I therefore almost do not have any motivation but sheer curiosity.)
According to Peter May, there was a "folklore" notion of categorical subdivision in the 1960's. I learnt about it by Matias del Hoyo's paper cited by Roman Bruckner in his comment to Peter May's answer. If I am mot mistaken, this notion had appeared in Anderson's paper "Fibrations and Geometric Realizations" as well as a paper authored by Dwyer and Kan, "Function complexes for diagrams of simplicial sets".
Who introduced the notion of subdivision of a (small) category? Are there any early references other than the two aforementioned papers?
Del Hoyo claims that performing the subdivision of a small category amounts to taking the nerve, applying Kan's simplicial subdivision functor, and coming back in $Cat$ by applying nerve's left-adjoint. Unfortunately, he does not prove this result. (I have discussed about this fact with him recently. If my memory serves me right, among other things, he proves that Anderson's and Dwyer-Kan's notions are equivalent.) Georges Maltsiniotis has given a rough proof of the verification to me. I was at that time unable to find any published proof. Even if it is an easy "folklore" result, I think it would be useful to have a proof publicly available somewhere.
Is there a published proof of the fact that this categorical subdivision is merely the composition of three well-known functors as above? Was it also "common knowledge" in the 1960's?
Finally, I cannot help asking a question which had come to my mind at that time, but to which I have not devoted much consideration since then. Using higher categorical nerves, there is an "obvious" definition of what could be analogs of this construction for higher categories. Therefore:
Have "higher analogs" of this categorical subdivision been studied?