4 citations · 4 across the 1 of their papers we have counts for
5 papers
Homotopical categories: from model categories to -categories
Emily Riehl
This chapter, written for "Stable categories and structured ring spectra," edited by Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill, surveys the history of homotopical cat…
On the construction of limits and colimits in -categories
Emily Riehl, Dominic Verity
In previous work, we introduce an axiomatic framework within which to prove theorems about many varieties of infinite-dimensional categories simultaneously. In this paper, we estab…
Recognizing quasi-categorical limits and colimits in homotopy coherent nerves
Emily Riehl, Dominic Verity
In this paper we prove that various quasi-categories whose objects are -categories in a very general sense are complete: admitting limits indexed by all simplicial sets. Th…
Categorical notions of fibration
Fosco Loregian, Emily Riehl
Fibrations over a category , introduced to category theory by Grothendieck, encode pseudo-functors , while the special case of discrete fibrat…
Multivariable adjunctions and mates
Eugenia Cheng, Nick Gurski, Emily Riehl
We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is t…