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THE UNITY AND IDENTITY OF DECIDABLE OBJECTS AND DOUBLE-NEGATION SHEAVES

Published online by Cambridge University Press:  21 December 2018

MATÍAS MENNI
MATÍAS MENNI*
Affiliation:
CONICET AND UNIVERSIDAD NACIONAL DE LA PLATA LA PLATA1900ARGENTINAE-mail: matias.menni@gmail.com
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Abstract

Let ${\cal E}$ be a topos, ${\rm{Dec}}\left( {\cal E} \right) \to {\cal E}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg \,\,\neg }} \to {\cal E}$ be the full subcategory of double-negation sheaves. We give sufficient conditions for the existence of a Unity and Identity ${\cal E} \to {\cal S}$ for the two subcategories of ${\cal E}$ above, making them Adjointly Opposite. Typical examples of such ${\cal E}$ include many ‘gros’ toposes in Algebraic Geometry, simplicial sets and other toposes of ‘combinatorial’ spaces in Algebraic Topology, and certain models of Synthetic Differential Geometry.

Keywords

18B2518F9903E99axiomatic cohesiontopos theoryset theory

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1667 - 1679
Copyright
Copyright © The Association for Symbolic Logic 2018 

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