Algebra/Topology seminar

Speaker: Steve Lack

Title: Enriched and ordinary accessible categories

Abstract: Locally presentable categories (also known as presentable categories) are particularly well-behaved complete and cocomplete categories in which questions such as the representability of functors and the existence of adjoints become more tractable. Accessible categories are a generalization of these where completeness and cocompleteness are not assumed. They are precisely those categories which can be sketched, in the sense of Ehresmann. Examples include the non-complete categories of fields, of Hilbert spaces, of linearly ordered sets, and of monoidal categories.

There is a well-developed theory of local presentability for enriched categories, enriched accessible categories (such as the 2-category of monoidal categories) have received much less attention.

I will give an introduction to accessibility both for ordinary and for enriched categories.