The homotopy category has as objects the vertices of C. Quasistatic approximation s refers to different domains and different meanings. Homotopy theory Higher category theory. This page was last edited on 23 December , at

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In classical electromagnetism , there are at least two consistent quasistatic approximations of Maxwell equations: Often, however, one may want to calculate the magnetic field due to time varying currents accelerating charge or other forms of moving charge. Strictly speaking, in these cases the aforementioned equations are invalid, as the field measured at the observer must incorporate distances measured at the retarded time , that is the observation time minus the time it took for the field traveling at the speed of light to reach the observer.

The retarded time is different for every point to be considered, hence the resulting equations are quite complicated; often it is easier to formulate the problem in terms of potentials; see retarded potential and Jefimenko's equations. In this point of view the quasistatic approximation is obtained by using time instead of retarded time or equivalently to assume that the speed of light is infinite. To first order, the mistake of using only Biot—Savart's law rather than both terms of Jefimenko's magnetic field equation fortuitously cancel.

From Wikipedia, the free encyclopedia. Retrieved 5 February Retrieved from " https: Thus, in a quasi-category, one cannot define a composition law on morphisms, since one can choose many ways to compose maps.

In other words, while the composition law is not uniquely defined, it is unique up to a contractible choice. Given a quasi-category C, one can associate to it an ordinary category hC, called the homotopy category of C.

The homotopy category has as objects the vertices of C. The morphisms are given by homotopy classes of edges between vertices. From Wikipedia, the free encyclopedia. Free category Functor category Quotient category Product category Subcategory. Categorification Enriched category Higher-dimensional algebra Homotopy hypothesis Model category Simplex category.

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