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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.
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 ...
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 ...
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.
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 ...
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
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.