What are...(commuting) diagrams?

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

This time.
What are...(commuting) diagrams? Or: Graphs and paths.

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.

Warning.
1 and 5 should swap places at 4:33, thanks Spogel.

Slides.

Website with exercises.

Diagram.

Commutative diagram.

Mathematical diagram.

Pictures used.

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

Nlab.

TheCatsters.

Mathematica.

#categorytheory
#categoricalalgebra
#mathematics

[spogel]

many thanks for your excellent presentations. found perhaps only one minor typo: shouldn't 1 and 5 be changed at 4:33 ?

[tomwright]

It feels like a general graph is not a category. You need your graph to have some sort of transitivity