4 papers
Free fibrations, lax colimits and Kan extensions for -categories
Fernando Abellán, Rune Haugseng, Louis Martini
In the first part of this paper we study fibrations of -categories. We give a simple characterization of such fibrations in terms of a certain square being a pullback,…
Homotopical commutative rings and bispans
Bastiaan Cnossen, Rune Haugseng, Tobias Lenz +1
We prove that commutative semirings in a cartesian closed presentable -category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors fr…
Envelopes for Algebraic Patterns
Shaul Barkan, Rune Haugseng, Jan Steinebrunner
We generalize Lurie's construction of the symmetric monoidal envelope of an -operad to the setting of algebraic patterns. This envelope becomes fully faithful when sliced o…
Algebras for enriched -operads
Rune Haugseng
Using the description of enriched -operads as associative algebras in symmetric sequences, we define algebras for enriched -operads as certain modules in symmetric…