etale homotopy

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• Étale fundamental group — The étale fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces.Topological analogueIn algebraic topology, the fundamental group :pi 1(T) of a connected topological space T is… …   Wikipedia

• Topos — For topoi in literary theory, see Literary topos. For topoi in rhetorical invention, see Inventio. In mathematics, a topos (plural topoi or toposes ) is a type of category that behaves like the category of sheaves of sets on a topological space.… …   Wikipedia

• Pro-simplicial set — In mathematics, a pro simplicial set is an inverse system of simplicial sets.A pro simplicial set is called pro finite if each term of the inverse system of simplicial sets has finite homotopy groups.Pro simplicial sets show up in shape theory,… …   Wikipedia

• Michael Artin — in Berkeley Michael Artin (* 28. Juni 1934 in Hamburg) ist ein US amerikanischer Mathematiker mit Forschungsschwerpunkt in algebraischer Geometrie und Algebra. Biografie Michael Artin wurde 1934 als Sohn des berühmten Mathematikers …   Deutsch Wikipedia

• Jean-Louis Verdier — (1935 ndash; 1989) was a French mathematician who worked, under the guidance of Alexander Grothendieck, on derived categories and Verdier duality. He was a close collaborator of Alexander Grothendieck, notably contributing to SGA 4 his theory of… …   Wikipedia

• ГОМОТОПИЧЕСКИЙ ТИП — топологизированной категории проективная система топологич. пространств, ассоциированная с топологизированной категорией и позволяющая определять гомотопические группы этой категории, группы гомологии и когомологий со значениями в абелевой группе …   Математическая энциклопедия

• Barry Mazur — Barry Mazur. Barry Charles Mazur (* 19. Dezember 1937 in New York City) ist ein US amerikanischer Mathematiker, der auf dem Gebiet der Topologie, Zahlentheorie und arithmetischen algebraischen Geometrie arbeitet …   Deutsch Wikipedia

• Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …   Wikipedia

• Non-Hausdorff manifold — In mathematics, it is a usual axiom of a manifold to be a Hausdorff space, and this is assumed throughout geometry and topology: manifold means (second countable) Hausdorff manifold . In general topology, this axiom is relaxed, and one studies… …   Wikipedia

• Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a …   Wikipedia

• Fibration — In mathematics, especially algebraic topology, a fibration is a continuous mapping:p:E o B,satisfying the homotopy lifting property with respect to any space. Fiber bundles (over paracompact bases) constitute important examples. In homotopy… …   Wikipedia