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

In category theory, a branch of mathematics, a stable model category is a pointed model category in which the suspension functor is an equivalence of...

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked...

models of (∞, 1)-categories, including Segal category, simplicially enriched category, topological category, complete Segal space. A quasi-category is...

specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian...

prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for example they are regular...

In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent...

Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

related) categories, as discussed below. More generally, instead of starting with the category of topological spaces, one may start with any model category and...

initial reasons for the development of the theory of model categories: a model category M is a category in which there are three classes of maps; one of these...

In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more...

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...

the homotopy category. From the point of view of model categories, the derived category D(A) is the true 'homotopy category' of the category of complexes...

prediction and modeling is handled by computer numerical models such as ADCIRC and SLOSH. In 2012, the NHC extended the wind speed range for Category 4 by 1 mph...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...

The Rutherford model was devised by Ernest Rutherford to describe an atom. Rutherford directed the Geiger–Marsden experiment in 1909, which suggested...

In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e...

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas...

security models, see Category:Computer security models. Access control list (ACL) Attribute-based access control (ABAC) Bell–LaPadula model Biba model Brewer...

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

generic term for all models of (infinity, k) categories for any k. Simplicially enriched categories, or simplicial categories, are categories enriched over simplicial...

In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent...

In atomic physics, the Bohr model or Rutherford–Bohr model was the first successful model of the atom. Developed from 1911 to 1918 by Niels Bohr and building...

In category theory, a Kleisli category is a category naturally associated to any monad T. It is equivalent to the category of free T-algebras. The Kleisli...

2003), known professionally as Kōki (stylized as Kōki,), is a Japanese model and songwriter. Mitsuki Kimura was born on February 5, 2003, in Tokyo, Japan...

more general spaces is part of the subject of shape theory. In any model category, a weak equivalence between cofibrant-fibrant objects is a homotopy...

In category theory, a branch of mathematics, a (left) Bousfield localization of a model category replaces the model structure with another model structure...

In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms:...