October 16, 2025Open Access

Extension Monads: Some Structure Theorems

Key Points

Extension monads commute with direct product operations, enhancing algebraic understanding and applications.
Key finding includes only trivial retractions from either enlargement or extension monads in algebra structures.
The research elaborates on structure results related to infinitely many finitary operations in algebra categories.
Significant implications for theoretical studies in categories of algebras arise from these structure theorems.

Abstract

We investigate the behavior of extension monads, introduced in the 1990s by the second author, in terms of structure results for infinitely many finitary operations and common constructions in varieties or categories of algebras. Specifically, we see that for finite collections of algebras of the same signature there the extension monad operation commutes with the direct product operation, and that the only retractions from an enlargement or extension monad are trivial.

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Cite This Study

Bowerman et al. (Thu,) studied this question.

synapsesocial.com/papers/68f0f51d8dd8ea469b1d7135 https://doi.org/https://doi.org/10.48550/arxiv.2508.05828

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