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The theory was rounded out by establishing that a Grothendieck topos was a category of sheaves, where now the word sheaf had acquired an extended meaning, since it involved a Grothendieck topology. The idea of a Grothendieck topology (also known as a site ) has been characterised by John Tate as a bold pun on the two senses of Riemann surface .
Topos Theory. Courier. ISBN 978-0-486-49336-7. For a long time the standard compendium on topos theory. However, even Johnstone describes this work as "far too hard to read, and not for the faint-hearted." Johnstone, Peter T. (2002). Sketches of an Elephant: A Topos Theory Compendium. Vol. 2. Clarendon Press. ISBN 978-0-19-851598-2.
A locale is a sort of a space but perhaps not with enough points. [3] The topos theory is sometimes said to be the theory of generalized locales. [4]Jean Giraud's gros topos, Peter Johnstone's topological topos, [5] or more recent incarnations such as condensed sets or pyknotic sets.
Kleene, S. C. (1945). "On the interpretation of intuitionistic number theory". Journal of Symbolic Logic. 10 (4): 109–124. doi:10.2307/2269016. JSTOR 2269016. S2CID 40471120. Phoa, Wesley (1992). An introduction to fibrations, topos theory, the effective topos and modest sets (Technical report). Laboratory for Foundations of Computer Science ...
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Francis William Lawvere (/ l ɔː ˈ v ɪər /; February 9, 1937 – January 23, 2023) was an American mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
The classifying topos for linear orders with distinct largest and smallest elements of a topos is the topos of simplicial sets. If G is a discrete group, the classifying topos for G-torsors over a topos is the topos BG of G-sets. The classifying space of topological groups in homotopy theory.
In mathematics, a coherent topos is a topos generated by a collection of quasi-compact quasi-separated objects closed under finite products. [1] Deligne's completeness theorem says a coherent topos has enough points. [2] William Lawvere noticed that Deligne's theorem is a variant of the Gödel completeness theorem for first-order logic. [3]