nLab
sheaf and topos theory

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topos theory

Sketches of an Elephant

Background

Toposes

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

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The theory of toposes in general and of Grothendieck toposes – categories of sheaves – in particular.

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Revised on May 14, 2010 21:06:03 by Urs Schreiber (134.100.32.31)
Edit | Back in time (14 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: category theory, groupoid, isomorphism, higher category theory, enriched category theory, physics, morphism, category, object, natural transformation, functor, topos, (-1)-category, hypercover, presheaf, skeleton, infinity-stack, Lie infinity-groupoid, Cat, set, monoidal category, enriched category, end, Kan extension, (infinity,1)-category, 0-category, truth value, subobject classifier, representable functor, limit, cone, opposite category, hom-functor, global element, (n,r)-category, cover, weak factorization system, simplicial object, homotopy coherent category theory, orthogonal factorization system, free functor, 2008 changes, projective object, copower, power, nerve, image, geometric realization, regular epimorphism, Yoneda lemma, adjoint functor, orthogonality, split epimorphism, regular monomorphism, colimit, profunctor, model structure on simplicial presheaves, split monomorphism, connection on a cubical set, weighted limit, partial order, Isbell envelope, fundamental group of a topos, adjoint functor theorem, kernel, cokernel, Higher Topos Theory, abelian category, universal construction, exact functor, cocone, additive and abelian categories, (infinity,1)-category of (infinity,1)-sheaves, (infinity,1)-presheaf, (infinity,1)-topos, Sheaves in Geometry and Logic, injective object, cohomology, (infinity,1)-sheaf, decidable equality, Godement product, co-Yoneda lemma, derived stack, coreflective subcategory, quasicoherent sheaf, hypercompletion, (infinity,1)-category of (infinity,1)-presheaves, constant infinity-stack, structured (infinity,1)-topos, motivation for sheaves, cohomology and higher stacks, path category, Grothendieck construction, vector bundle, (1,0)-category, principal infinity-bundle, local model structure on simplicial presheaves, groupoid object in an (infinity,1)-category, essential image, cosmos, nerve and realization, models for infinity-stack (infinity,1)-toposes, Verity on descent for strict omega-groupoid valued presheaves, geometry (for structured (infinity,1)-toposes), effective epimorphism, 2009 August changes, universal colimits, Cartesian morphism, Ieke Moerdijk, Saunders Mac Lane, single-sorted definition of a category, (infinity,1)-topos - contents, n-localic (infinity,1)-topos, (0,1)-category, category theory - contents, homotopy groups in an (infinity,1)-topos, Whitehead theorem, hypercomplete (infinity,1)-topos, monadicity theorem, nPOV, open cover, covering, categorical homotopy groups in an (infinity,1)-topos, reflective sub-(infinity,1)-category, SSet-site, model site, locally constant infinity-stack, (n,1)-topos, Postnikov tower in an (infinity,1)-category, category of presheaves, (infinity,1)-site, topological localization, shape of an (infinity,1)-topos, tangent category, Whitehead tower in an (infinity,1)-topos, n-connected object of an (infinity,1)-topos, hypercomplete object, Isbell conjugation, embedding, effective monomorphism, sifted category, groupal model for universal principal infinity-bundles, universal principal infinity-bundle, Freyd-Mitchell embedding theorem, indecomposable object, function algebras on infinity-stacks, split hypercover