Model category information

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

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

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...

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

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...

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 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, a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle...

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

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

In category theory, a branch of mathematics, a closed category is a special kind of category. In a locally small category, the external hom (x, y) maps...

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...

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

the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is an extension of the concept...

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

In mathematics, the simplex category (or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order-preserving...

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

quotient category is a category obtained from another category by identifying sets of morphisms. Formally, it is a quotient object in the category of (locally...

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general...

In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures...