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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 …
Lennart Meier's user avatar
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}\ …
Lennart Meier's user avatar
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 …
Lennart Meier's user avatar
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 …
Lennart Meier's user avatar