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math.CT2026
Hammock localization via Segal animae
Kensuke Arakawa, Bastiaan Cnossen
We give a short, conceptual account of Dwyer--Kan's hammock localization in the setting of -categories. Starting from Mazel-Gee's formula for localization via the relative…
math.AT2026
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…
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…