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.

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 quasiisomorphisms. Both of them seemed to be some sort of quotienting/equivalenceclasslike action, so why not do them at the same time? What different roles were played by each step?
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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.
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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.
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[See part 1 here and part 2 here]
This post is a weird one: it’s not really aimed at any one audience, but is more of a dump of a bunch of information that I’m trying to process.
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categorytheory 
algebraictopology 
spectra 
operads 
homotopytheory 
birds 
quicktip 
questions 
quantumphysics 
quantumcomputing 
differentialgeometry 
complexgeometry
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