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For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.
15
votes
Accepted
Three questions on $\operatorname{hocolim}$
First question$\newcommand{\op}[1]{{#1}^{\mathrm{op}}}$$\newcommand{\sSet}{\mathrm{sSet}}$$\newcommand{\Grpd}{\mathrm{Grpd}}$$\newcommand{\Cat}{\mathrm{Cat}}$$\newcommand{\NN}{\mathbb{N}}$$\newcommand …
3
votes
Accepted
Can we invert barycentric subdivision?
[As requested by Vidit Nanda, I am reposting a slightly edited version of my comment above as an answer. Nevertheless, I hope someone will eventually give a satisfactory answer to this question.]
The …
3
votes
Simplicial replacements in smoothing theory
I present here a reference for Peter May's comment to Tom Goodwillie's answer in this thread. It also corroborates the comment by John Klein below the question stating that there is no obvious topolog …
2
votes
Multisimplicial geometric realization
[This answer is mostly a long comment to Peter May's answer.]
Edit: I have corrected some arrows which were pointing the wrong way.$\newcommand{\real}[1]{\lvert #1\rvert}
\newcommand{\Map}{\operatorn …