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Homotopy theory, homological algebra, algebraic treatments of manifolds.
8
votes
Joins of simplicial sets
It might be helpful to work through some simple examples. You probably know that Δn ★ Δk = Δn+k+1. This has to do with the ordinal sum: one way of defining joins is as a restriction of the monoidal st …
23
votes
How canonical is cofibrant replacement?
I don't know the answer to your questions off the top of my head, but I think algebraic weak factorization systems (the new consensus terminology for what were originally called natural weak factoriza …