Soichiro Fujii

activity

20242026

collaborators

8 papers

cs.LO2026

Monads and Distributive Laws in Substructural Contexts (Extended Version)

Soichiro Fujii, Yun Chen Tsai, YoÃ v Montacute +1

We present a categorical theory of monads and distributive laws in substructural contexts. In the study of distributive laws, the roles of (the absence of) structural rules for var…

math.CT2026

Nerves of generalized multicategories

Soichiro Fujii, Stephen Lack

For any category $E$ and monad $T$ thereon, we introduce the notion of $T$ -simplicial object in $E$ . Any $T$ -category in the sense of Burroni induces a $T$ -si…

math.CT2025

$I ¨ $ -equifibrations between strict and weak $I ¨ $ -categories

Soichiro Fujii, Keisuke Hoshino, Yuki Maehara

We study $I ¨ $ -equifibrations between weak $I ¨ $ -categories in the sense of Batanin--Leinster. We define $I ¨ $ -equifibrations as a natural weak $I ¨ $ -categorical analogue of isofibrati…

math.CO2025

Homotopy types of Hom complexes of graph homomorphisms whose codomains are square-free

Soichiro Fujii, Kei Kimura, Yuta Nozaki

Given finite simple graphs $G$ and $H$ , the Hom complex $Hom (G, H)$ is a polyhedral complex having the graph homomorphisms $G \to H$ as the vertices. We determine the homoto…

math.CT2025

The familial nature of enrichment over virtual double categories

Soichiro Fujii, Stephen Lack

Originally enriched categories were defined over a monoidal category, but it was gradually realized that important examples can only be included when one enriches over more general…

math.CO2025

Homotopy types of Hom complexes of graph homomorphisms whose codomains are cycles

Soichiro Fujii, Yuni Iwamasa, Kei Kimura +2

For simple graphs $G$ and $H$ , the Hom complex $Hom (G, H)$ is a polyhedral complex whose vertices are the graph homomorphisms $G \to H$ and whose edges connect the pairs of…