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Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Topos theory" The following 17 pages are in this category, out of 17 total.
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 .
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 ...
In mathematics, a topos (US: / ˈ t ɒ p ɒ s /, UK: / ˈ t oʊ p oʊ s, ˈ t oʊ p ɒ s /; plural topoi / ˈ t ɒ p ɔɪ / or / ˈ t oʊ p ɔɪ /, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site).
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 ...
In his 2000 article "Comments on the Development of Topos Theory", Lawvere discusses his motivation for simplifying and generalizing Grothendieck's concept of a topos. He explains that his interest stemmed from his earlier studies in physics, particularly the foundations of continuum physics as inspired by Truesdell, Noll, and others. He notes ...
Roughly an ∞-topos is an ∞-category which looks like the ∞-category of all homotopy types. In a topos mathematics can be done. In a higher topos not only mathematics can be done but also "n-geometry", which is higher homotopy theory. The topos hypothesis is that the (n+1)-category nCat is a Grothendieck (n+1)-topos. Higher topos theory ...