Homotopy extension property information

the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space. The homotopy extension...

particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting property or the covering...

The homotopy lifting property is used to characterize fibrations. Another useful property involving homotopy is the homotopy extension property, which...

normal) then every closed subspace of X {\displaystyle X} has the homotopy extension property with respect to any absolute neighborhood retract. Likewise,...

in geometry Field extension, in Galois theory Group extension, in abstract algebra and homological algebra Homotopy extension property, in topology Kolmogorov...

at most n. Using then the homotopy extension property to extend this to a homotopy on all of X, and patching these homotopies together, will finish the...

In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on...

Hepatoerythropoietic porphyria, a blood disease High-energy physics Homotopy extension property, a property in algebraic topology Humane endpoint, predetermined stopping...

involves cohomology groups with coefficients in homotopy groups to define obstructions to extensions. For example, with a mapping from a simplicial complex...

purposes of homotopy theory. Specifically, the category of simplicial sets carries a natural model structure, and the corresponding homotopy category is...

associated to the site underlying a topos a pro-simplicial set (up to homotopy). (It's better to consider it in Ho(pro-SS); see Edwards) Using this inverse...

space Winding number Simply connected Universal cover Monodromy Homotopy lifting property Mapping cylinder Mapping cone (topology) Wedge sum Smash product...

Grothendieck's homotopy hypothesis states that the ∞-groupoids are spaces. If we model our ∞-groupoids as Kan complexes, then the homotopy types of the...

a universal property is a property that characterizes up to an isomorphism the result of some constructions. Thus, universal properties can be used for...

Kan extensions are universal constructs in category theory, a branch of mathematics. They are closely related to adjoints, but are also related to limits...

of A, B, C. Then Exti R(A,B) can be identified with the group of chain homotopy classes of chain maps P → Q[i]. The Yoneda product is given by composing...

suitable set theoretic properties for the derived category, this time because these properties are already satisfied by the homotopy category. As noted before...

fundamental group based at x0, denoted π1(X, x0). This is the group of homotopy classes of loops based at x0, with the group operation of concatenation...

topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. The following are basic examples...

group of the circle has the homotopy-type of the orthogonal group O ( 2 ) {\displaystyle O(2)} . The corresponding extension problem for diffeomorphisms...

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'...

Simply connected Semi-locally simply connected Path (topology) Homotopy Homotopy lifting property Pointed space Wedge sum Smash product Cone (topology) Adjunction...

definition is very similar to that of fibrations in topology (see also homotopy lifting property), whence the name "fibration". Using the correspondence between...

In mathematics, and especially in homotopy theory, a crossed module consists of groups G {\displaystyle G} and H {\displaystyle H} , where G {\displaystyle...

is an active area of research, one direction being the development of homotopy type theory. The first computer proof assistant, called Automath, used...