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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

15 votes

Why are monads useful?

I would say first that monads are useful in that they offer a level of abstraction that can be used to describe lots of different algebraic phenomena. That is, categories of groups, abelian groups, ri …
6 votes

Computations in $\infty$-categories

I believe that many computations could be done in the context of $\infty$-categories given enough outside input. For example, I would expect that most of the spectral sequences arising in topology cou …
Justin Noel's user avatar
  • 1,738
5 votes
Accepted

Bousfield-Kan: Cosimplicial Replacement of a fibration of diagrams is a fibration?

First I would like to refer you Goerss and Jardine's book "Simplicial homotopy theory" as an alternative resource, with modern typesetting. In particular, Example VII.4.2 gives a construction of the c …
Justin Noel's user avatar
  • 1,738