Holmstrom MacLane cohomology

MacLane cohomology

Jibladze and Pirashvili showed that MacLane homology of a ring A and module M can be interpreted as $Tor_*^{\mathcal{F}}(A \otimes , M \otimes)$ in the category $\mathcal{F}$ of functors from the category of f.g. free A-modules to the category of A-modules. Similarly for MacLane cohomology, but with $Ext$ intstead.

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MacLane cohomology

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MacLane cohomology

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MacLane cohomology

CT (Category theory), NCG (Algebra and noncommutative geometry)

nLab page on MacLane cohomology