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6 papers
Enriched homotopy-coherent structures
Hongyi Chu, Rune Haugseng
We introduce a general notion of enrichment for homotopy-coherent algebraic structures described by Segal conditions, using the framework of "algebraic patterns" developed in our p…
On rectification and enrichment of infinity properads
Hongyi Chu, Philip Hackney
We develop a theory of infinity properads enriched in a general symmetric monoidal infinity category. These are defined as presheaves, satisfying a Segal condition and a Rezk compl…
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…
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…
Enriched -operads
Hongyi Chu, Rune Haugseng
In this paper we initiate the study of enriched -operads. We introduce several models for these objects, including enriched versions of Barwick's Segal operads and the dend…
Two models for the homotopy theory of -operads
Hongyi Chu, Rune Haugseng, Gijs Heuts
We compare two models for -operads: the complete Segal operads of Barwick and the complete dendroidal Segal spaces of Cisinski and Moerdijk. Combining this with comparison…