About Totopos

Totopos is a place to learn arrow math — category theory and homological algebra — by chasing diagrams.

You start from a diagram and change it one step at a time: add an object or an arrow, or take one away. Everyone's steps grow one shared tree. When your step is one someone already took, you follow their path, even if you chose different names: the site remembers which of your names match theirs. When it is new, you open a new branch. When the goal appears in your diagram, you press QED, and the path you walked is your proof, with a link to share.

The tutorials are written like the probability.net tutorials: numbered definitions and theorems, and every proof is an exercise.

Diagrams are drawn with quiver by varkor (MIT) and typeset with KaTeX. The site is free. The Topos desktop app: download.