#model categories

[mathematikerin-freyja]

I hope that when I get into a math phd position I get to take algebraic topology as a course. I want to go in having already familiarised myself with (infinity, 1)-categories and model categories, but no actual concrete examples of either, and then just torment the lecturer with my questions and comments. "Oh shit so this is like a cofibrant replacement in real life! Huh, cute."

[aufenthaltsraumspizza]

Only homotopy kids will get this.

[uncontrolledprocrastination]

Sometime soon, I need to sort out which parts of algebraic topology are purely (model) category theoretic and which are specific to the category of spaces. For instance, the Mather Cube Theorems seem to be topoi-theoretic, so might not apply to an arbitrary model category. There's just so much going on in this subject!