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A Formal Approach to Generalisations of Monads

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If you have a question about this talk, please contact José Siqueira.

Monads are endofunctors endowed with a structure that emulates that of a monoid. They were first defined on categories, but this notion can be generalised. For example we can consider pseudomonads on 2-categories, which are monads with diagrams commutative up to coherent isomorphisms (Blackwell, Kelly, Power, etc). Another possible generalisation is relative monads, which are not endofunctors but have a similar structure to monads.

In “The formal theory of monads” Street studies monads in a formal way, i.e. defining them in a general 2-category. In this talk we will recall some aspects of Street’s work and show how they can be extended to pseudo and relative monads.

This talk is part of the Category Theory Seminar series.

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