group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
By a generalized cohomology theory is usually meant a contravariant functor on a homotopy category satisfying all abstract properties of ordinary cohomology, except possibly for the dimension axiom. For more on this see at
Whitehead-generalized cohomology.
(and for the dual concept see at generalized homology).
But there are more general generalizations of the concept of ordinary cohomology, too. For instance there is also
etc.
For a fully general concept of generalized cohomology, see at
homotopy | cohomology | homology | |
---|---|---|---|
$[S^n,-]$ | $[-,A]$ | $(-) \otimes A$ | |
category theory | covariant hom | contravariant hom | tensor product |
homological algebra | Ext | Ext | Tor |
enriched category theory | end | end | coend |
homotopy theory | derived hom space $\mathbb{R}Hom(S^n,-)$ | cocycles $\mathbb{R}Hom(-,A)$ | derived tensor product $(-) \otimes^{\mathbb{L}} A$ |
Last revised on November 29, 2021 at 07:04:48. See the history of this page for a list of all contributions to it.