9 citations · 19 across the 12 of their papers we have counts for
12 papers
Quillen-McCord theorem for persistence finite posets
Vitalii Guzeev, Kohei Tanaka
In this paper, we establish a persistence version of the Quillen-McCord theorem for persistence finite posets. Given a map between persistence finite pos…
Strong homotopy types of acyclic categories and -complexes
Kohei Tanaka
We extend the homotopy theories based on point reduction for finite spaces and simplicial complexes to finite acyclic categories and -complexes, respectively. The functors of cl…
Discrete Morse theory and classifying spaces
Vidit Nanda, Dai Tamaki, Kohei Tanaka
The aim of this paper is to develop a refinement of Forman's discrete Morse theory. To an acyclic partial matching on a finite regular CW complex , Forman introduced a discr…
A combinatorial description of topological complexity for finite spaces
Kohei Tanaka
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original f…
Minimal networks for sensor counting problem using discrete Euler calculus
Kohei Tanaka
This paper proposes a method to reduce noise in acyclic sensor networks enumerating targets using the integral theory with respect to Euler characteristic. For an acyclic network (…
Discrete Euler integration over functions on finite categories
Kohei Tanaka
This paper provides the theory of integration with respect to Euler characteristics of finite categories. As an application, we use sensors to enumerate the targets lying on a pose…
Čech complexes for covers of small categories
Kohei Tanaka
We present a combinatorial analogue of the nerve theorem for covers of small categories, using the Grothendieck construction. We apply our result to prove the inclusion-exclusion p…
Classical and quantum conditional measures from a categorical viewpoint
Hitoshi Motoyama, Kohei Tanaka
This paper presents categorical structures on classical measure spaces and quantum measure spaces in order to deal with canonical maps associated with conditional measures as morph…
The Euler characteristic of a bicategory and the product formula for fibered bicategories
Kohei Tanaka
This paper studies the Euler characteristic of a bicategory based on the concept of magnitudes introduced by Leinster. We focus on its invariance with respect to biequivalence and…
The Euler characteristic of an enriched category
Kazunori Noguchi, Kohei Tanaka
We define Euler characteristic of a category enriched by a monoidal model category. If a monoidal model category V is equipped with Euler characteristic that is compatible with wea…
Reconstruction of Manifolds from Their Morse Functions
Kohei Tanaka
This paper describes how to recover the topology of a closed manifold from a good Morse function on . The essential method was suggested by Cohen, Jones and Segal. They…
A model structure on the category of small categories for coverings
Kohei Tanaka
We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant obje…