Ringed topos
In mathematics, a ringed topos is a generalization of a ringed space; that is, the notion is obtained by replacing a "topological space" by a "topos". The notion of a ringed topos has applications to
List object
In category theory, an abstract branch of mathematics, and in its applications to logic and theoretical computer science, a list object is an abstract definition of a list, that is, a finite ordered s
Quasitopos
In mathematics, specifically category theory, a quasitopos is a generalization of a topos. A topos has a subobject classifier classifying all subobjects, but in a quasitopos, only strong subobjects ar
Natural numbers object
In category theory, a natural numbers object (NNO) is an object endowed with a recursive structure similar to natural numbers. More precisely, in a category E with a terminal object 1, an NNO N is giv
Nisnevich topology
In algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which has been used in algebraic K-theory, A¹
Lawvere–Tierney topology
In mathematics, a Lawvere–Tierney topology is an analog of a Grothendieck topology for an arbitrary topos, used to construct a topos of sheaves. A Lawvere–Tierney topology is also sometimes also calle
∞-topos
In mathematics, an ∞-topos is, roughly, an ∞-category such that its objects behave like sheaves of spaces with some choice of Grothendieck topology; in other words, it gives an intrinsic notion of she
Coherent topos
In mathematics, a coherent topos is a topos generated by a collection of quasi-compact quasi-separated objects closed under finite products.
Grothendieck topology
In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological space. A category together with
History of topos theory
This article gives some very general background to the mathematical idea of topos. This is an aspect of category theory, and has a reputation for being abstruse. The level of abstraction involved cann
Topos
In mathematics, a topos (UK: /ˈtɒpɒs/, US: /ˈtoʊpoʊs, ˈtoʊpɒs/; plural topoi /ˈtoʊpɔɪ/ or /ˈtɒpɔɪ/, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (
Presheaf (category theory)
In category theory, a branch of mathematics, a presheaf on a category is a functor . If is the poset of open sets in a topological space, interpreted as a category, then one recovers the usual notion
Fundamental theorem of topos theory
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 in then there is a functor whic
Étale topos
In mathematics, the étale topos of a scheme X is the category of all étale sheaves on X. An étale sheaf is a sheaf on the étale site of X.
Subobject classifier
In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω. In typica
Classifying topos
In mathematics, a classifying topos for some sort of structure is a topos T such that there is a natural equivalence between geometric morphisms from a cocomplete topos E to T and the category of mode
Effective topos
In mathematics, the effective topos is a topos introduced by Martin Hyland, based on Kleene's notion of recursive realizability, that captures the idea of effectivity in mathematics.