Cohomology of diagrams of algebras
Michael Robinson

TL;DR
This paper develops a cohomology theory for diagrams of algebras using Beck's comonad approach and introduces a spectral sequence linking diagram cohomology to algebra cohomology.
Contribution
It extends cohomology theory to diagrams of algebras and applies it to $\\Psi$-rings, establishing a spectral sequence connecting diagram and algebra cohomology.
Findings
Established a spectral sequence relating diagram cohomology to algebra cohomology.
Applied the theory specifically to the case of $\Psi$-rings.
Provided a framework for computing cohomology of algebra diagrams.
Abstract
We consider cohomology of diagrams of algebras by Beck's approach, using comonads. We then apply this theory to computing the cohomology of -rings. Our main result is that there is a spectral sequence connecting the cohomology of the diagram of an algebra to the cohomology of the underlying algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
