group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
An object in an (∞,1)-topos is said to have cohomological dimension if all cohomology groups of degree vanish on that object.
For an (∞,1)-topos and , an object is said to have cohomological dimension if for all Eilenberg-MacLane objects for the cohomology of with these coefficients vanishes:
We say the (∞,1)-topos itself has cohomological dimension if its terminal object does.
This appears as HTT, def. 7.2.2.18.
If has homotopy dimension then it also has cohomology dimension .
The converse holds if has finite homotopy dimension and .
This appears as HTT, cor. 7.2.2.30.
notion of dimension
The general -topos-theoretic notion is discussed in section 7.2.2 of
Last revised on January 20, 2024 at 10:33:27. See the history of this page for a list of all contributions to it.