46 citations · 283 across the 29 of their papers we have counts for
4 papers · 2 filters
Homotopy coherent adjunctions and the formal theory of monads
Emily Riehl, Dominic Verity
In this paper, we introduce a cofibrant simplicial category that we call the free homotopy coherent adjunction and characterize its n-arrows using a graphical calculus that we deve…
Six model structures for DG-modules over DGAs: Model category theory in homological action
Tobias Barthel, J. P. May, Emily Riehl
In Part 1, we describe six projective-type model structures on the category of differential graded modules over a differential graded algebra A over a commutative ring R. When R is…
The 2-category theory of quasi-categories
Emily Riehl, Dominic Verity
In this paper we redevelop the foundations of the category theory of quasi-categories (also called infinity-categories) using 2-category theory. We show that Joyal's strict 2-categ…
The theory and practice of Reedy categories
Emily Riehl, Dominic Verity
The goal of this paper is to demystify the role played by the Reedy category axioms in homotopy theory. With no assumed prerequisites beyond a healthy appetite for category theoret…