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  2. History of topos theory - Wikipedia

    en.wikipedia.org/wiki/History_of_topos_theory

    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 .

  3. Fundamental theorem of topos theory - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    In mathematics, The fundamental theorem of topos theory states that the slice / of a topos over any one of its objects is itself a topos. Moreover, if there is a morphism f : A → B {\displaystyle f:A\rightarrow B} in E {\displaystyle \mathbf {E} } then there is a functor f ∗ : E / B → E / A {\displaystyle f^{*}:\mathbf {E} /B\rightarrow ...

  4. Category:Topos theory - Wikipedia

    en.wikipedia.org/wiki/Category:Topos_theory

    This page was last edited on 17 September 2019, at 05:32 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  5. William Lawvere - Wikipedia

    en.wikipedia.org/wiki/William_Lawvere

    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.

  6. Topos - Wikipedia

    en.wikipedia.org/wiki/Topos

    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.

  7. Effective topos - Wikipedia

    en.wikipedia.org/wiki/Effective_topos

    An introduction to fibrations, topos theory, the effective topos and modest sets (Technical report). Laboratory for Foundations of Computer Science, University of Edinburgh. CiteSeerX 10.1.1.112.4533. ECS-LFCS-92-208. Bernadet, Alexis; Graham-Lengrand, Stéphane (2013). "A simple presentation of the effective topos". arXiv: 1307.3832 .

  8. Coherent topos - Wikipedia

    en.wikipedia.org/wiki/Coherent_topos

    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]

  9. ∞-topos - Wikipedia

    en.wikipedia.org/wiki/%E2%88%9E-topos

    A theorem of Lurie [2] states that an ∞-category is an ∞-topos if and only if it satisfies an ∞-categorical version of Giraud's axioms in ordinary topos theory. A "topos" is a category behaving like the category of sheaves of sets on a topological space. In analogy, Lurie's definition and characterization theorem of an ∞-topos says that ...