113 citations · 354 across the 32 of their papers we have counts for
5 papers · 2 filters
Two-variable fibrations, factorisation systems and -categories of spans
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
We prove a universal property for -categories of spans in the generality of Barwick's adequate triples, explicitly describe the cocartesian fibration corresponding to the s…
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
We provide a calculus of mates for functors to the -category of -categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformat…
On distributivity in higher algebra I: The universal property of bispans
Elden Elmanto, Rune Haugseng
Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of (-)categorie…
On (co)ends in -categories
Rune Haugseng
In this short note we prove that two definitions of (co)ends in -categories, via twisted arrow -categories and via -categories of simplices, are equivalent.…
On lax transformations, adjunctions, and monads in -categories
Rune Haugseng
We use the basic expected properties of the Gray tensor product of -categories to study (co)lax natural transformations. Using results of Riehl-Verity and Zaganidis we…