Representing the language of a Topos as a Quotient of the Category of Spans

M. Golshani and A. Shiralinasab Langari

We use quotients of span categories to introduce the language of a topos. We also introduce the notion of logical relation and study the quotients of span categories derived from them. As an application we show that the category of Boolean toposes is a reflective subcategory of the category of toposes, when the morphisms are logical functors.

Keywords: Language of topos, Span category, Allegory, Topos, Boolean Topos

2020 MSC: 18A32, 18B99, 18C10, 03G30

Theory and Applications of Categories, Vol. 44, 2025, No. 27, pp 805-825.

Published 2025-09-01.

http://www.tac.mta.ca/tac/volumes/44/27/44-27.pdf

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