2023/11/21 by Nadia Romero, Romero, Nadia
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2311.12269
Let R be a commutative ring with unit. We develop a Hochschild cohomology theory in the category F of linear functors defined from an essentially small symmetric monoidal category enriched in R-Mod, to R-Mod. The category F is known to be symmetric monoidal too, so one can consider monoids in F and modules over these monoids, which allows for the possibility of a Hochschild cohomology theory. The emphasis of the article is in considering natural hom constructions appearing in this context. These homs, together with the abelian structure of F lead to nice definitions and provide effective tools to prove the main properties and results of the classical Hochschild cohomology theory.