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Questions tagged [derived-categories]

For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.

41 votes
7 answers
4k views

Simplicial objects

How should one think about simplicial objects in a category versus actual objects in that category? For example, both for intuition and for practical purposes, what's the difference between a [...
Kevin H. Lin's user avatar
  • 20.9k
5 votes
4 answers
804 views

$E_\infty$ spectrum corresponding to $\Bbb Z_p$

First of the questions about derived algebraic geometry from a noobie. The way I understand it, every discrete ring $R$ corresponds to some ring spectrum whose $\pi_0$ is $R$. Now consider $p$-adic ...
Ilya Nikokoshev's user avatar
19 votes
5 answers
4k views

Derived categories and homotopy categories

There are two constructions that look quite similar to me: the derived category of an abelian category, and the homotopy category of a model category. Is there any explicit relationship between these ...
Kevin H. Lin's user avatar
  • 20.9k

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