# nLab generalized cohomology

cohomology

### Theorems

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

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

homotopycohomologyhomology
$[S^n,-]$$[-,A]$$(-) \otimes A$
category theorycovariant homcontravariant homtensor product
homological algebraExtExtTor
enriched category theoryendendcoend
homotopy theoryderived hom space $\mathbb{R}Hom(S^n,-)$cocycles $\mathbb{R}Hom(-,A)$derived tensor product $(-) \otimes^{\mathbb{L}} A$

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