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For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
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 …
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}\ …
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 …
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 …