Revisiting Burroni's T-categories
Walter Tholen (York University)
Abstract: Following the appearance of Lambek’s multicategories and Barr’s presentation of topological spaces as relational T-algebras, Albert Burroni introduced T-categories and T-functors in 1971. They provide an overarching environment for the general study of algebras and spaces, which encompasses elements of monad theory, internal category theory, and categorical topology.
In this talk we have a fresh look at Burroni’s paper and point to the Street-Walters comprehensive factorization system for functors and the (antiperfect, perfect) factorization system for continuous maps of Tychonoff spaces to demonstrate that, despite its generality, Burroni’s setting allows for the establishment of non-trivial results and the discovery of unexpected connections between seemingly unrelated theorems.
(Joint work with Leila Yeganeh)
category theory
Audience: researchers in the topic
Series comments: ItaCa Fest is an online webinar aimed to gather the community of ItaCa.
| Organizer: | Progetto ItaCa* |
| *contact for this listing |