Recognisable languages over monads

In this talk, I will discuss extensions of semigroups, which are defined using Eilenberg-Moore algebras over monads. The methodology is that one designs a monad around a chosen kind of object, e.g. words, trees or graphs. Once the monad has been defined, abstract nonsense is employed to automatically get notions such as “semigroup/algebra”, “term”, “equation”, “pseudovariety”, “profinite”, etc. Some of the more generic theorems also get automatically proved, e.g. the Eilenberg Pseudovariety Theorem, or the Reiterman Theorem.

This talk is based on the draft monograph

Date and Venue

Start Date
Online Zoom meeting
End Date


Mikołaj Bojańczyk

Speaker's Institution

University of Warsaw



Semigroups, Automata and Languages