The Unification of Mathematics via Topos Theory

DOI10.1007/978-3-030-94452-0_30arXiv1006.3930MaRDI QIDQ6075162

Olivia Caramello

Publication date: 20 September 2023

Published in: Studies in Universal Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.3930

zbMATH Keywords

Morita equivalencebridgeGrothendieck toposgeometric theoryclassifying toposunifying theorysubtopostopos-theoretic invariant

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Categorical logic, topoi (03G30) Topoi (18B25) History of mathematics in the 19th century (01A55) Theories (e.g., algebraic theories), structure, and semantics (18C10) History of Chinese mathematics (01A25) General logic (03Bxx)

Cites Work

• Unnamed Item
• A characterization theorem for geometric logic
• Atomic toposes and countable categoricity
• De Morgan classifying toposes
• De Morgan's law and the theory of fields
• Sheaves in geometry and logic: a first introduction to topos theory
• First order categorical logic. Model-theoretical methods in the theory of topoi and related categories
• Representing topoi by topological groupoids
• Fraïssé's construction from a topos-theoretic perspective
• Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
• Theories, Sites, Toposes
• Lattices of theories
• Yoneda representations of flat functors and classifying toposes
• Universal models and definability

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