What is Coherency (homotopy theory)?

In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric...

In finance, the greater fool theory suggests that one can sometimes make money through the purchase of overvalued assets — items with a purchase price drastically exceeding the intrinsic value — if those assets...

Laser theory of Fabry-Perot semiconductor lasers proves to be nonlinear, since the gain, the refractive index and the loss coefficient are the functions of energy flux. The nonlinear theory made...

In theoretical physics, there are many theories with supersymmetry which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion.

Mixture theory is used to model multiphase systems using the principles of continuum mechanics generalised to several interpenetrable continua. The basic assumption is that, at any instant of time, all...

Punctuated equilibrium in social theory is a conceptual framework for understanding the process of change in complex social systems. The approach studies the evolution of policy change, including the evolution...

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

In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space....

In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property is a technical condition on a continuous function from a topological space E to another one,...

In algebraic topology, a fiber-homotopy equivalence is a map over a space B that has homotopy inverse over B It is a relative analog of a homotopy equivalence between spaces....