Search results
Results from the WOW.Com Content Network
Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Pages in category "Topos theory" The following 17 pages are in this category, out ...
What results is essentially an intuitionistic (i.e. constructive logic) theory, its content being clarified by the existence of a free topos. That is a set theory, in a broad sense, but also something belonging to the realm of pure syntax. The structure on its sub-object classifier is that of a Heyting algebra.
Higher Topos Theory covers two related topics: ∞-categories and ∞-topoi (which are a special case of the former). The first five of the book's seven chapters comprise a rigorous development of general ∞-category theory in the language of quasicategories, a special class of simplicial set which acts as a model for ∞-categories.
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, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory.There are several insights that allow for such a reformulation.
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 ...
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 ...
Alternative PDF with hyperlinks) Lurie, Jacob (2009). Higher Topos Theory. Princeton University Press. arXiv: math.CT/0608040. ISBN 978-0-691-14048-3. As PDF. nLab, the collective and open wiki notebook project on higher category theory and applications in physics, mathematics and philosophy