5 papers
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…
Homotopy-coherent algebra via Segal conditions
Hongyi Chu, Rune Haugseng
Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an "algebraic pattern", bywhich we mean an -category equipped with…
Shifted Coisotropic Correspondences
Rune Haugseng, Valerio Melani, Pavel Safronov
We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks where the -morphism…
Segal spaces, spans, and semicategories
Rune Haugseng
We show that Segal spaces, and more generally category objects in an -category , can be identified with associative algebras in the double -category of…