2 citations · 2 across the 8 of their papers we have counts for
4 papers · 1 filter
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…