Representing the language of a topos as quotient of the category of spans

2022/01/24 by Mohammad Golshani, Golshani, M., Langari, A. Shiralinasab
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2201.09551

openalex publication_date 2022/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use quotients of span categories to introduce the language of a topos. We also study the logical relations and 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.

Related

• Elementary topoi
• Topoi of automata I: Four topoi of automata and regular languages
• A Very Short Introduction to Topos Theory (adapted from Prof. Pettigrew's notes)
• Logic and Concepts in the 2-category of Topoi
• The topology of syntax relations of a formal language