Aaron Mazel-Gee

activity

20092024

most citedQuillen adjunctions induce adjunctions of quasicategories

41 citations · 121 across the 22 of their papers we have counts for

collaborators

Showing 2015 · math.ATShow all

4 papers · 2 filters

math.AT2015★ 2 cited

Model $\infty$ -categories III: the fundamental theorem

Aaron Mazel-Gee

We prove that a model structure on a relative $\infty$ -category $(M, W)$ gives an efficient and computable way of accessing the hom-spaces $h o m_{M [[W^{- 1}]]} (x, y)$ in the localizati…

math.AT2015★ 3 cited

Model $\infty$ -categories II: Quillen adjunctions

Aaron Mazel-Gee

We prove that various structures on model $\infty$ -categories descend to corresponding structures on their localizations: (i) Quillen adjunctions; (ii) two-variable Quillen adjunct…

math.AT2015★ 13 cited

All about the Grothendieck construction

Aaron Mazel-Gee

We provide, among other things: (i) a Bousfield--Kan formula for colimits in $\infty$ -categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps betw…

math.AT2015★ 8 cited

The universality of the Rezk nerve

Aaron Mazel-Gee

We functorially associate to each relative $\infty$ -category $(R, W)$ a simplicial space $N_{\infty}^{R} (R, W)$ , called its Rezk nerve (a straightforward generalization of Rezk's "classi…

Model ∞-categories III: the fundamental theorem

Model ∞-categories II: Quillen adjunctions

All about the Grothendieck construction

The universality of the Rezk nerve

Model $\infty$ -categories III: the fundamental theorem

Model $\infty$ -categories II: Quillen adjunctions