Generalised homomorphisms, measuring coalgebras and extended symmetries
Marjorie Batchelor, Will Boulton, Daren Chen, Jonathan Rawlinson and, Mustafa Warsi
TL;DR
This paper introduces generalized homomorphisms for algebra categories, explores their relations via the Sweedler product, and develops a parallel module theory, providing tools for calculating universal measuring coalgebras.
Contribution
It extends the concept of algebra homomorphisms, establishes a hom-tensor equivalence using the Sweedler product, and develops a parallel theory for modules.
Findings
Categories of generalized algebra homomorphisms are described.
A hom-tensor equivalence via the Sweedler product is established.
Tools for calculating universal measuring coalgebras are provided.
Abstract
Three categories of algebras with morphisms generalising the usual set of algebra homomorphisms are described. The Sweedler product provides a hom-tensor equivalence relating these three categories, and a tool enabling the universal measuring coalgebra to be calculated in small cases. A parallel theory for modules is presented.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology