Nuclei of categories with tensor products

TL;DR

This paper explores the concept of nuclei within monoidal categories, drawing parallels to non-associative algebras, and examines nuclei of module categories as a key example.

Contribution

It introduces a categorical construction of nuclei inspired by algebraic analogies, extending the concept to monoidal categories and their module categories.

Findings

Nuclei can be constructed categorically analogous to algebraic nuclei.

The paper provides examples involving module categories.

It establishes a framework for analyzing non-associative structures categorically.

Abstract

Following the analogy between algebras (monoids) and monoidal categories the construction of nucleus for non-associative algebras is simulated on the categorical level. Nuclei of categories of modules are considered as an example.