nLab Ryuya Hora

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Selected writings

On Lawvere’s first problem in topos theory, the existence of a proper class of quotient toposes of a Grothendieck topos (with ‘quotient maps’ defined to be ‘connected surjective geometric morphisms’):

Solution for the case of Boolean toposes:

• Ryuya Hora: Internal Parameterization of Hyperconnected Quotients [arXiv:2302.06851]

A special example in the non-Boolean case:

• Ryuya Hora, Yuhi Kamio: Quotient toposes of discrete dynamical systems [arXiv:2310.02647]

Full solution:

• Yuhi Kamio, Ryuya Hora, A solution to the first Lawvere’s problem A Grothendieck topos that has a proper class many quotient topoi [arXiv:2407.17105]

On Lawvere’s fourth problem in topos theory, to calculate the Aufhebung of the opposition between skeleta and coskeleta in the category of symmetric simplicial sets (the category of presheaves on the category of non-empty finite sets):

• Ryuya Hora, Yuki Maehara: Lawvere’s fourth open problem: Levels in the topos of symmetric simplicial sets [arXiv:2503.03439]

On adjoint strings of functors between a topos and Set and specifically on completely connected toposes (locally connected toposes with a further left adjoint to the left adjoint to the inverse image functor):

• Ryuya Hora: Grothendieck topos with a left adjoint to a left adjoint to a left adjoint to the global sections functor [arXiv:2503.04317]

category: people