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Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.

20 votes
Accepted

Is the $\infty$-category of spectra “convenient”?

My colleague Dylan answered first (I keep telling him not to spend too much time on this toy :) but I both agree and disagree with his "Yes of course". The same words are used with different meanings …
Peter May's user avatar
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4 votes

$t$-structure on modules over highly structured ring spectra

I don't have time to think carefully. However, I answered this question for the sphere $G$-spectrum here: A heart for stable equivariant homotopy theory. I see no problem in generalizing that answer …
Community's user avatar
  • 1
20 votes
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A category with weak equivalences that is not a model category

A very interesting example: consider semi-simplicial sets (alias $\Delta$-sets). These are simplicial sets without degeneracies, and there is an ``adjoin degeneracies'' functor from semi-simplicial se …
Peter May's user avatar
  • 30.4k