2 citations · 2 across the 8 of their papers we have counts for
8 papers
Games as recursive coalgebras: A categorical view on the Nim-sum
Ryuya Hora
In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this que…
Normalization of a subgroup, in a topos, and of a word-congruence
Ryuya Hora
This paper provides a new categorical definition of a normalization operator motivated by topos theory and its applications to algebraic language theory. We first define a normaliz…
Lawvere's fourth open problem: Levels in the topos of symmetric simplicial sets
Ryuya Hora, Yuhi Kamio, Yuki Maehara
In the topos of simplicial sets, it makes sense to ask the following question about a given natural number : what is the minimum value such that -skeletality implies -…
Grothendieck topoi with a left adjoint to a left adjoint to a left adjoint to the global sections functor
Ryuya Hora
This paper introduces the notion of complete connectedness of a Grothendieck topos, defined as the existence of a left adjoint to a left adjoint to a left adjoint to the global sec…
Topoi of automata I: Four topoi of automata and regular languages
Ryuya Hora
Both topos theory and automata theory are known for their multi-faceted nature and relationship with topology, algebra, logic, and category theory. This paper aims to clarify the t…
Solution to Lawvere's first problem: a Grothendieck topos that has proper class many quotient topoi
Yuhi Kamio, Ryuya Hora
This paper solves the first of the open problems in topos theory posted by William Lawvere, concerning the existence of a Grothendieck topos that has proper class many quotient top…
Quotient toposes of discrete dynamical systems
Ryuya Hora, Yuhi Kamio
This paper gives a classification of classes of discrete dynamical systems (a set equipped with an endofunction) closed under finite limits and small colimits. The conclusion is si…
Internal Parameterization of Hyperconnected Quotients
Ryuya Hora
One of the most fundamental facts in topos theory is the internal parameterization of subtoposes: the bijective correspondence between subtoposes and Lawvere-Tierney topologies. In…