Embedding of pseudotensor category

TL;DR

This paper constructs an algebraic embedding functor from pseudotensor to tensor categories for module categories, utilizing operadic methods to develop associated Schur functors and free objects.

Contribution

It provides a purely algebraic realization of the embedding functor for pseudotensor categories of modules, extending previous definitions by Beilinson and Drinfeld.

Findings

Constructed an algebraic embedding functor from pseudotensor to tensor categories.

Developed operadic methods to build Schur functors and free objects.

Extended the understanding of module categories in tensor category theory.

Abstract

We realize the embedding functor from pseudotensor category to tensor category in a purely algebraic setting when the pseudotensor category is the category $\mathcal{M}(H)$ of left $H$-modules, which is originally defined by Beilinson and Drinfeld. Then we use operadic methods to construct the Schur functor and free object in the tensor category.