homotopy diagram

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• Homotopy lifting property — In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a… …   Wikipedia

• Homotopy category of chain complexes — In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences. It lies intermediate between the category of chain… …   Wikipedia

• Spectrum (homotopy theory) — In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. There are several different constructions of categories of spectra, all of which give the same homotopy category.Suppose we… …   Wikipedia

• Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… …   Wikipedia

• Double groupoid — In mathematics, especially in higher dimensional algebra and homotopy theory, a double groupoid generalises the notion of groupoid and of category to a higher dimension. Contents 1 Definition 2 Convolution algebra 3 Double Groupoid Category …   Wikipedia

• Mapping cylinder — In mathematics, specifically algebraic topology, the mapping cylinder of a function f between topological spaces X and Y is the quotient where the union is disjoint, and ∼ is the equivalence relation That is, the mapping cylinder Mf …   Wikipedia

• Seifert–van Kampen theorem — In mathematics, the Seifert–van Kampen theorem of algebraic topology, sometimes just called van Kampen s theorem, expresses the structure of the fundamental group of a topological space X, in terms of the fundamental groups of two open, path… …   Wikipedia

• Triangulated category — A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t category is a triangulated category with a t… …   Wikipedia

• List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

• Michael J. Hopkins — Mike Hopkins in Oberwolfach 2009 Born April 18, 1958 …   Wikipedia

• Functor — For functors as a synonym of function objects in computer programming to pass function pointers along with its state, see function object. For the use of the functor morphism presented here in functional programming see also the fmap function of… …   Wikipedia