group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Given any generalized (Eilenberg-Steenrod) cohomology theory $E$, then for each topological space $X$, there is, by definition, the graded abelian group
This is the $E$-cohomology group of $X$. Now if $E$ is a multiplicative cohomology theory, then these groups inherit the structure of rings. As such
is the $E$-cohomology ring of $X$.
Analogously for various suitable generalizations of the nature of $E$ and $X$ (see at generalized cohomology).
Implementation of ordinary$\;$cohomology rings in cubical agda:
Thomas Lamiaux, Axel Ljungström, Anders Mörtberg, Computing Cohomology Rings in Cubical Agda, CPP 2023: Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs (2023) [arxiv:2212.04182, doi:10.1145/3573105.3575677]
Thomas Lamiaux: Computing Cohomology Rings in Cubical Agda, talk at Running HoTT 2024, CQTS@NYUAD (April 2024) [video:kt]
Last revised on July 13, 2024 at 07:51:30. See the history of this page for a list of all contributions to it.