Seminário de Álgebras de Hopf e Categorias Monoidais
RELATION MORPHISMS OF DIRECTED GRAPHS
Prof. Dr. Piotr M. Hajac (IMPAN-Warsaw)
Abstract: Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same time, one needs a new category of graphs that allows a “common denominator” functor unifying the covariant and contravariant constructions. In this talk, I will show how to solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. I will illustrate relation morphisms of graphs by the naturally occurring example of including Cuntz algebras into matrices over Cuntz algebras. Based on joint work with Gilles G. de Castro and Francesco D’Andrea.
Data e Horário: Segunda feira, dia 18 de agosto de 2025, 16:00h
Local: Auditório Airton Silva, Departamento de Matemática – MTM /CFM