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Start Over Descriptor "Mathematics - Category Theory" Language portuguese
2 results on '"Mathematics - Category Theory"'

1. Variedades de \'algebras topologicas

Author

Earl, Lucas

Subjects
Mathematics - Category Theory
Abstract

Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that capture group properties. We then observe the results about topological groups now extended to varieties of topological algebras. We conclude showing that for topological algebras obeying certain axioms, there exist semi-direct products which we caracterize like in [17]., Comment: Master's thesis, in Portuguese

Published
2013

2. Quantity vs. size in representation theory

Author

Vitória, Jorge

Subjects
Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Category Theory, Category Theory (math.CT), Mathematics - Rings and Algebras, Representation Theory (math.RT), Mathematics - Representation Theory
Abstract

In this note, we survey two instances in the representation theory of finite-dimensional algebras where the quantity of a type of structures is intimately related to the size of those same structures. More explicitly, we review the fact that (1) a finite-dimensional algebra admits only finitely many indecomposable modules up to isomorphism if and only if every indecomposable module is finite-dimensional; (2) the category of modules over a finite-dimensional algebra admits only finitely many torsion classes if and only if every torsion class is generated by a finite-dimensional module., Comment: Invited survey to a special issue of the "Boletim da Sociedade Portuguesa de Matem\'atica", aimed at a general audience. This work does not contain any new results

Published
2020

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