Geodesic
A category of arrow algebras for modified realizability
Theory and applications of categories, Tome 44 (2025), pp. 132-180.

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In this paper we further the study of arrow algebras, simple algebraic structures inducing toposes through the tripos-to-topos construction, by defining appropriate notions of morphisms between them which correspond to morphisms of the associated triposes. Specializing to geometric inclusions, we characterize subtriposes of an arrow tripos in terms of nuclei on the underlying arrow algebra, recovering a classical locale-theoretic result. As an example of application, we lift modified realizability to the setting of arrow algebras, and we establish its functoriality.
Publié le :
Classification : 03G30, 18B25
Keywords: arrow algebras, topos theory, geometric morphisms, realizability 
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     author = {Umberto Tarantino},
     title = {A category of arrow algebras for modified realizability},
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     year = {2025},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2025_44_a3/}
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Umberto Tarantino. A category of arrow algebras for modified realizability. Theory and applications of categories, Tome 44 (2025), pp. 132-180. http://geodesic.mathdoc.fr/item/TAC_2025_44_a3/