An initial solution to the monad problem, and then some more

This is the second of two talks about monads, based on the very good notes by Andrea Schalk and continuing the one I gave on the 30th of May. Recall that we are trying to solve the following problem:

given a monad , find an adjunction such that and

If the adjunction solves the problem above, we say that it generates the monad .

The first solution to this problem was given by the Swiss mathematician Heinrich Kleisli, and is based on an alternative way of defining monads, as it is the case with adjunctions.

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When does an endofunctor derive from an adjunction?

This is the first of two talks based on Andrea Schalk’s very good introduction to monads, which can be retrieved HERE

In the following, if is a category, we indicate by the collection of objects of , and by the collection of morphisms in from to .

As we know, there are two basic ways of defining an adjunction:

Finite trees as initial algebra

In the last Theory Lunch session I talked about a category theoretic approach to finite trees.

What is the correct definition of ideal monads?

This was the third and final lunch in my series about ideal monads. I talked about how to define ideal monads correctly. My talk was based on a discussion with Tarmo Uustalu.

An introduction to ideal monads

Based on my recap of monads from the week before, I talked about ideal monads.

A short recap of monads

I used the first theory lunch meeting at the Institute of Cybernetics to recap some basics about monads. I discussed how monads are defined in category theory, and how they are implemented in Haskell.