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Results tagged with descent
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user 402
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votes
Accepted
The derived category does not satisfy descent - example
Consider the canonical functor $H$ from the homotopy category of homotopy coherent descent data in the ∞-category of coherent sheaves
to the category of descent data in the derived category of coherent … Indeed, by modifying the above example appropriately, we can construct descent data for the derived category
in which the composition of homotopies $h$ is not homotopic to the identity homotopy,
which …
- 37.8k
2
votes
Accepted
Is there any relation between two pseudofunctors associated to two different cleavages of th...
Two different cleavages produce isomorphic pseudofunctors.
This follows immediately from Theorem 8.3.1
in Borceux's Handbook of Categorical Algebra 2.
Specifically, part (1) of this theorem states
t …
- 37.8k
5
votes
Non-trivial automorphisms and descent
Question 3: What is the idea of an effective descent morphism? … objects on $\cF$ equipped with a descent data. …
- 37.8k