An Embedding theorem for abelian monoidal categories
Phung Ho Hai
TL;DR
This paper proves that under certain conditions, abelian categories can be embedded into bimodule categories over rings, with a detailed study of semisimple rigid monoidal categories.
Contribution
It establishes an embedding theorem for abelian monoidal categories into bimodule categories, extending understanding of their structure.
Findings
Abelian categories can be embedded into bimodule categories under technical conditions.
Semisimple rigid monoidal categories are analyzed in detail.
Provides a framework for representing abelian monoidal categories via bimodules.
Abstract
We show that, with some technical conditions, an abelian category can be embedded into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology