RELATION MORPHISMS OF DIRECTED GRAPHS

Speaker(s)

GILLES GONÇALVES DE CASTRO

Affiliation

Universidade Federal de Santa Catarina, Florianópolis, Brazil

Language of the talk

English

Date

June 11, 2025, 5:15 p.m.

Information about the event

IMPAN 405 & ZOOM

Title in Polish

RELATION MORPHISMS OF DIRECTED GRAPHS

Seminar

North Atlantic Noncommutative Geometry Seminar

---

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 many naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls. Time permitting, I will explain how to look at relation morphisms from the point of view of groupoids. Based on joint works with Francesco D'Andrea, Piotr M. Hajac and Ralf Meyer.

 

---