TL;DR
This paper explores modules over generalized bialgebra structures, viewing them as quantum analogues of profunctors between small categories, thereby extending the understanding of quantum categorical frameworks.
Contribution
It introduces and studies modules over quantum categories, bialgebroids, and weak bialgebras, framing them as quantum analogues of profunctors between small categories.
Findings
Modules over quantum structures are characterized as quantum profunctors.
The paper establishes foundational properties of these modules.
It connects quantum algebraic structures with categorical concepts.
Abstract
There are various generalizations of bialgebras to their ''many object'' versions, such as quantum categories, bialgebroids and weak bialgebras. These can also be thought of as quantum analogues of small categories. In this paper we study modules over these structures, which are quantum analogues of profunctors (also called distributors) between small categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra