nLab Kensuke Arakawa

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Selected writings

On marked simplicial sets:

• Kensuke Arakawa: Classification Diagrams of Marked Simplicial Sets [arXiv:math/2311.01101]

On homotopy limits and homotopy colimits of chain complexes (cf. model structure on chain complexes):

• Kensuke Arakawa: Homotopy Limits and Homotopy Colimits of Chain Complexes, J. Pure Appl. Algebra 230 4 (2026) 108232 [doi:10.1016/j.jpaa.2026.108232, arXiv:2310.00201]

Showing that monoidal relative categories model monoidal $(\infty,1)$-categories:

• Kensuke Arakawa: Monoidal Relative Categories Model Monoidal $\infty$-Categories [arXiv:2504.20606]

On localization of $(\infty,1)$-categories and the relative Rezk nerve:

• Kensuke Arakawa, Bastiaan Cnossen: A short proof of the universality of the relative Rezk nerve, Proc. Amer. Math. Soc. 154 5 (2026) 1849–1853 [arXiv:2505.14123, doi:10.1090/proc/17483]

Showing that relative operads model $(\infty,1)$-operads:

• Kensuke Arakawa, Victor Carmona, Francesca Pratali: Relative operads model $\infty$-operads [arXiv:2512.16374]

Related entries

• Bousfield–Kan formula

category: people