3 papers
math.CT2026
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…
math.CT2025
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.
math.CT2025
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…