What is…Beck’s monadicity theorem?

Goal.
Explaining basics concepts of category theory in an intuitive way.

This time.
What is…Beck’s monadicity theorem? Or: Categories via actions.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Disclaimer.
The distinction between “large classes” and “small classes (sets)” turns out is crucial for many categorical considerations, but somehow makes the language more cumbersome without too much gain imho. So I will strategically ignore all set-theoretical issues.

Slides.

Beck’s monadicity theorem.

Barr-Beck (same game, different name).

Monads.

Pictures used.

Some books I am using (I sometimes steal some pictures from there).

Nlab.

TheCatsters.

Mathematica.

#categorytheory
#categoricalalgebra
#mathematics