Approximate Hagemann-Mitschke co-operations

TL;DR

This paper extends the concept of approximate Mal'tsev co-operations to n-permutable categories with binary coproducts, broadening the applicability of varietal techniques in category theory.

Contribution

It introduces approximate Hagemann-Mitschke co-operations, generalizing previous notions and extending characterization theorems to a wider class of categories.

Findings

Generalization of varietal techniques to n-permutable categories

Extension of characterization theorems for n-permutable varieties

Introduction of approximate Hagemann-Mitschke co-operations

Abstract

We show that varietal techniques based on the existence of operations of a certain arity can be extended to n-permutable categories with binary coproducts. This is achieved via what we call approximate Hagemann-Mitschke co-operations, a generalisation of the notion of approximate Mal'tsev co-operation. In particular, we extend characterisation theorems for n-permutable varieties due to J. Hagemann and A. Mitschke to regular categories with binary coproducts.