Zobrazeno 1 - 10
of 57
pro vyhledávání: '"MAEHARA,Yuki"'
We study $\omega$-weak equivalences between weak $\omega$-categories in the sense of Batanin-Leinster. Our $\omega$-weak equivalences are strict $\omega$-functors satisfying essential surjectivity at every dimension, and when restricted to those betw
Externí odkaz:
http://arxiv.org/abs/2406.13240
Autor:
Campion, Timothy, Maehara, Yuki
We construct a (lax) Gray tensor product of $(\infty,2)$-categories and characterize it via a model-independent universal property. Namely, it is the unique monoidal biclosed structure on the $\infty$-category of $(\infty,2)$-categories which agrees
Externí odkaz:
http://arxiv.org/abs/2304.05965
Publikováno v:
Higher Structures 8(2):386-415, 2024
We study weakly invertible cells in weak $\omega$-categories in the sense of Batanin-Leinster, adopting the coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $\omega$-category are closed under globular pasti
Externí odkaz:
http://arxiv.org/abs/2303.14907
We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for ($n$-trivial, saturated) comical sets to the category of marked simplicial set equipped with a model structure for ($n$-trivia
Externí odkaz:
http://arxiv.org/abs/2106.09428
Autor:
Maehara, Yuki
Publikováno v:
Journal of Pure and Applied Algebra, vol.227(3), 107230, 2023
The orientals are the free strict $\omega$-categories on the simplices introduced by Street. The aim of this paper is to show that they are also the free weak $\omega$-categories on the same generating data. More precisely, we exhibit the Street nerv
Externí odkaz:
http://arxiv.org/abs/2102.09736
We propose a new model for the theory of $(\infty,n)$-categories (including the case $n=\infty$) in the category of marked cubical sets with connections, similar in flavor to complicial sets of Verity. The model structure characterizing our model is
Externí odkaz:
http://arxiv.org/abs/2005.07603
Autor:
Maehara, Yuki
Publikováno v:
Advances in Mathematics 377 (2021) 107461
We construct an $(\infty,2)$-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an $n$-ary) functor on the category of $\Theta_2$-sets, and it is shown to be left Quillen with respect to Ara's mo
Externí odkaz:
http://arxiv.org/abs/2003.11757
Autor:
Maehara, Yuki
Publikováno v:
Advances in Mathematics 363 (2020) 107003
Dimitri Ara's 2-quasi-categories, which are certain presheaves over Andr\'{e} Joyal's 2-cell category $\Theta_2$, are an example of a concrete model that realises the abstract notion of $(\infty,2)$-category. In this paper, we prove that the 2-quasi-
Externí odkaz:
http://arxiv.org/abs/1902.08720
Publikováno v:
In Advances in Mathematics 1 March 2023 416
