This blog is a collection of reading notes of things that I try to learn. Often they are nothing more than summaries of various pages on the nLab, but collated, (over)simplified, and reordered to be more easily understood by, e.g., me. There will almost certainly be mistakes and bad viewpoints, so caveat lector.

• ## Derived, DG, triangulated, and infinity-categories

This post assumes that you have seen the construction of derived categories and maybe the definitions of dg- and $A_\infty$-categories, and wondered how they all linked together. In particular, as an undergraduate I was always confused as to what the difference was between the two steps of constructing the derived category of chain complexes was: taking equivalence classes of chain homotopic complexes; and then formally inverting all quasi-isomorphisms. Both of them seemed to be some sort of quotienting/equivalence-class-like action, so why not do them at the same time? What different roles were played by each step?

• ## Triangulations of products of triangulations

At a conference this week, I ended up having a conversation with Nicolas Vichery and Eduard Balzin about why simplices are the prevalent choice of geometric shape for higher structure, as opposed to e.g. cubes or globes.

• ## Quantum circuits (Part 1)

I am not at all a physicist, and my knowledge of quantum physics in particular comes solely from undergraduate courses that I followed years ago, and any reading I can get done when feeling mathematical but not inclined to work on my thesis. However, after scanning through some papers by Bartlett, Baez, Lauda, and Lurie, my interest in quantum physics, and quantum computing especially, has come back with a vengeance.