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.

An idea that came up in a few talks at CT2019 was that of ‘spans whose left leg is a left adjoint’. I managed (luckily) to get a chance to ask Mike Shulman a few questions about this, as well as post in
#math.CT:matrix.org
. What follows are some things that I learnt (mostly from [BD86]).Continue reading ⇾

I have just come back from CT2019 in Edinburgh, and it was a fantastic week. There were a bunch of really interesting talks, and I had a chance to meet some lovely people. I also got to tell people about
#math.CT:matrix.org
, and so hopefully that will start to pick up in the nottoodistant future.Continue reading ⇾

I haven’t posted anything in a while, and rather than trying to write about maths, I wanted to just share some lovely photos of Skomer island (which I recently visited). I am even less knowledgeable about birds than I am about maths, but I do love them, and this was the first time in my life that I’d actually seen a puffin in the flesh!
Continue reading ⇾

Having recently been thinking about twisting cochains (a major part of my thesis) a bit more, I think I better understand one reason why they are very useful (and why they were first introduced by Bondal and Kapranov), and that’s in ‘fixing’ a small quirk about dgcategories that I didn’t quite understand way back when I wrote this post about derived, dg, and $A_\infty$categories and their role in ‘homotopy things’.
This isn’t a long post and could probably instead be a tweet but then this blog would be a veritable ghost town.
Continue reading ⇾

categorytheory 
algebraictopology 
spectra 
operads 
homotopytheory 
birds 
quicktip 
questions 
quantumphysics 
quantumcomputing 
differentialgeometry 
complexgeometry
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