On the cap product in Hochschild theory

TL;DR

This paper provides an axiomatic framework for understanding the cap product in Hochschild theory and offers an interpretation using chain maps for associative unital algebras over a commutative ring.

Contribution

It introduces an axiomatic characterization of the cap product and interprets it through chain maps, advancing the theoretical understanding of Hochschild theory.

Findings

Axiomatic description of the cap product

Chain map interpretation of the cap product

Enhanced understanding of Hochschild algebra structures

Abstract

In this paper we give an axiomatic characterization of the cap product in the Hochschild theory of associative unital algebras which are projective over a commutative unital ring. We also give an interpretation of the cap product with coefficients in the algebra via chain maps.