A Functorial Approach to Gabrielk-quiver Constructions for Coalgebras and Pseudocompact Algebras

Autor(es)

Iusenko, Kostiantyn ^[1] ; MacQuarrie, John William ^[2] ; Quirino, Samuel ^{[2, 1]}

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP - Brazil

^[2] Univ Fed Minas Gerais, Belo Horizonte, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 52, n. 3, p. 697-719, SEP 2021.
• Citações Web of Science: 0

Resumo

We define the path coalgebra and Gabriel quiver constructions as functors between the category ofk-quivers and the category of pointedk-coalgebras, forka field. We define a congruence relation on the coalgebra side, show that the functors above respect this relation, and prove that the induced Gabrielk-quiver functor is left adjoint to the corresponding path coalgebra functor. We dualize, obtaining adjoint pairs of functors (contravariant and covariant) for pseudocompact algebras. Using these tools we describe precisely to what extent presentations of coalgebras and pseudocompact algebras in terms of path objects are unique, giving an application to homogeneous algebras. (AU)

• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático