7 papers
Relative dendroidal Rezk nerve and applications
Kensuke Arakawa, Victor Carmona, Francesca Pratali
We extend the dendroidal Rezk nerve to the setting of relative -operads. Our main theorem relates it to localization of -operads, generalizing a theorem of Mazel-Ge…
On the equivalence of two approaches to multiplicative homotopy theories
Kensuke Arakawa
We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal -categories and combinatorial symmetric monoidal model categori…
Monoidal Relative Categories Model Monoidal -Categories
Kensuke Arakawa
We prove that the homotopy theory of monoidal relative categories is equivalent to that of monoidal -categories, and likewise in the symmetric monoidal setting. As an appli…
Homotopy Limits and Homotopy Colimits of Chain Complexes
Kensuke Arakawa
We give a formula for homotopy limits and homotopy colimits of diagrams of chain complexes using the cobar and bar constructions, also known as the Bousfield--Kan formula. Along th…
A short proof of the universality of the relative Rezk nerve
Kensuke Arakawa, Bastiaan Cnossen
We give a concise, conceptual proof of the universality of the relative Rezk nerve, due to Mazel-Gee.
Classification diagrams of simplicial categories
Kensuke Arakawa
We show that the classification diagram of a relative -category arising from a relative simplicial category is equivalent to the levelwise nerve. Applications include the c…