Holmstrom Triple cohomology

Triple cohomology

This is the same as Monad cohomology

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Triple cohomology

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Triple cohomology

CT (Category theory), NCG

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Triple cohomology

Simplicial methods and the interpretation of triple cohomology. Gives a nice overview over how triple cohomology allows for a unified view on cohomology of algebraic objects.

LNM0080 introduction. Def, example (Godement) of sheaf cohomology, and more.

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Triple cohomology

Lots of material in LNM0080. A pair of adjoint functors $F: A \to B$, $U: B \to A$gives rise to a simplicial resolution of an object $X$ in $B$. Applying “appropriate coeff functors” to this resolution gives homology and cohomology theories. When the adjoint pair is tripleable, these enjoy nice properties such as classification of extensions and principal homogeneous objects. Relation to derived functor theories - triple cohomology must not vanish on injective coeffs apparently.

nLab page on Triple cohomology