- injective object
- мат.инъективный объект
English-Russian scientific dictionary. 2008.
injective object
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Injective object — In mathematics, especially in the field of category theory, the concept of injective object is a generalization of the concept of injective module. This concept is important in homotopy theory and in theory of model categories. The dual notion is … Wikipedia
Injective module — In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z module Q of all rational numbers. Specifically, if Q is a submodule of some… … Wikipedia
Injective hull — This article is about the injective hull of a module in algebra. For injective hulls of metric spaces, also called tight spans, injective envelopes, or hyperconvex hulls, see tight span. In mathematics, especially in the area of abstract algebra… … Wikipedia
Injective metric space — In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L∞ distances in higher dimensional vector spaces. These properties can … Wikipedia
Injective sheaf — In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext .). There is a further group of related concepts applied to sheaves: flabby … Wikipedia
Injective cogenerator — In category theory, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality. Generators are objects which cover other objects as an approximation, and (dually) cogenerators are objects which envelope other… … Wikipedia
Projective object — In category theory, the notion of a projective object generalizes the notion of free module.An object P in a category C is projective if the hom functor: operatorname{Hom}(P, )colonmathcal{C} omathbf{Set}preserves epimorphisms. That is, every… … Wikipedia
Derived category — In mathematics, the derived category D(C) of an abelian category C is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on C. The construction proceeds on the… … Wikipedia
Derived functor — In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. Contents 1 Motivation 2 Construction… … Wikipedia
Category of metric spaces — The category Met, first considered by Isbell (1964), has metric spaces as objects and metric maps or short maps as morphisms. This is a category because the composition of two metric maps is again metric.The monomorphisms in Met are the injective … Wikipedia
Category of rings — In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (preserving the identity). Like many categories in mathematics, the category of rings is… … Wikipedia
