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cohomology localization

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cohomology

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Definition

Let C be a stable (∞,1)-category (or (∞,1)-topos) and A∈C a stable coefficient object. For X∈C and n∈ℤ or (n∈ℕ) write

H n(X,A):=π 0C(X,B nA)H^n(X,A) := \pi_0 C(X, \mathbf{B}^n A)

for the cohomology of X with coefficients in A in degree n.

Say a morphism in C is A-local if it induces isomorphisms on all these cohomology groups. Let W be the class of all such morphisms.

Then the A-cohomology localization of C is – if it exists – the localization of an (∞,1)-category of C at W.

Examples

References

Set theoretic issues in cohomology localization – and their solution using large cardinal axioms such as Vopenka's principle, is discussed in

Revised on September 3, 2012 18:09:46 by Urs Schreiber (131.174.188.82)
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