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For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
38
votes
Do we still need model categories?
One nice feature of model categories is that you can speak also of the non-bifibrant objects (which is not longer possible, once you passed to the corresponding infinity-category). A few examples wher …
36
votes
What are Jacob Lurie's key insights?
I think, one of the key insights underlying derived algebraic geometry and Lurie's treatment of elliptic cohomology is taking some ideas of Grothendieck really serious. Two manifestations:
1) One of …
34
votes
2
answers
6k
views
Derived Algebraic Geometry and Chow Rings/Chow Motives
I recently heard a talk about Chow motives and also read Milne's exposition on motives. If I understand it correctly, the naive definition of the Chow ring would be that it simply consists of all alge …
8
votes
Colimits of cofibrations and homotopy colimits
In general, this is certainly not true. Take for example a space $X$ with an action by a group $G$. As a group acts by isomorphisms, it acts in particular by cofibrations. But the map $X/G \to X_{hG}\ …