As I mentioned in a previous post, I recently saw a talk by Rachel Hardeman on the A-homotopy theory of graphs, and it really intrigued me. In particular, it seemed to me that there was some nice structure that could be abstractified: that of a “graded homotopy structure”, as I’ve been calling it in my head. Rather than trying to type out everything in `#math.CT:matrix.org`

, I’ve decided to post it here, in the hope that I might be able to get some answers.

Posts tagged with homotopy-theory ← Return to all posts

Jul 19

#### Graded homotopy structures

Jul 19

#### Twisting cochains and twisted complexes

This week was the Young Topologists Meeting at EPFL in Lausanne, and had courses by Julie Bergner (on 1- and 2-Segal spaces) and Vidit Nanda (on the topology of data), as well as a bunch of great talks by various postdocs and PhD students. I was lucky enough to get the chance to talk about twisting cochains and twisted complexes for half an hour, and you can find the slides on my GitHub here.

Continue reading →Aug 18

#### Localisation and model categories (Part 1)

After some exceptionally enlightening discussions with Eduard Balzin recently, I’ve made some notes on the links between model categories, homotopy categories, and localisation, and how they all tie in together. There’s nothing particularly riveting or original here, but hopefully these notes can help somebody else who was lost in this mire of ideas.

Continue reading →