This is a continuation of the course "Monads and their applications". We will start with two-dimensional monad theory which, broadly speaking, is the study of categories equipped with algebraic structure. Specific examples are given by (enriched) categories with (symmetric or braided) monoidal structures and categories which admit certain limits or colimits. The morphisms of interest in these examples preserve the given structure only up to coherent isomorphism. For this reason, two-dimensional monad theory differs from the theory of monads enriched in categories discussed in the previous lecture. We will use the latter to study the former. Additional applications of monads that we will discuss are algebraic weak factorization systems and comonadic descent.

GRIPS (v3.9) wird vom RZ der Universität Regensburg betrieben. | Datenschutz | Kontakt | Impressum |