Noun:

ಅದೇ ಸಂಸ್ಥೆ,

homotopy's Usage Examples:

An important example is the standard model structure on simplicial sets: the associated homotopy category is equivalent to the homotopy category of topological spaces, even though simplicial sets are combinatorially defined objects that lack any topology.

nontrivial homotopy group.

Homotopy Kan extension The notion of homotopy Kan extension and hence in particular that of homotopy limit and homotopy colimit has a direct.

It is possible to describe the homotopy classes of maps from a CW-complex to BM.

In category theory, a branch of mathematics, Grothendieck"s homotopy hypothesis states that the ∞-groupoids are equivalent to the topological spaces.

Thus the naive homotopy category distinguishes spaces such as X and Y, whereas they become isomorphic in the homotopy category.

Singular cohomology has an even better property: it is a representable functor on the homotopy category.

Pointed versionOne useful variant is the homotopy category of pointed spaces.

homotopy coherently associative.

Indeed, all constant curvature manifolds have their universal cover to be either a sphere, or a [space], or \mathbb{R}^n, but \mathbb{CP}^n is simply-connected but not a sphere (for n>1), as can be seen for example from homotopy group calculations from long exact sequence of the fibration U(1)\to S^{2n+1}\to \mathbb{CP}^n.

Some topologists prefer instead to work with compactly generated weak Hausdorff spaces; again, with the standard model structure, the associated homotopy category is equivalent to the homotopy category of all topological spaces.

It is weaker than isotopy, and stronger than homotopy: isotopy implies concordance implies homotopy.

Vladimir (2008) "Motivic Eilenberg-Maclane spaces" The motivic Adams spectral sequence Motivic chromatic homotopy theory Jardine.