113 citations · 354 across the 32 of their papers we have counts for
6 papers · 1 filter
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.…
Free algebras through Day convolution
Hongyi Chu, Rune Haugseng
Building on the foundations in our previous paper, we study Segal conditions that are given by finite products, determined by structures we call cartesian patterns. We set up Day c…
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…