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Projective object information


In category theory, the notion of a projective object generalizes the notion of a projective module. Projective objects in abelian categories are used in homological algebra. The dual notion of a projective object is that of an injective object.

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Projective object

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category theory, the notion of a projective object generalizes the notion of a projective module. Projective objects in abelian categories are used in...

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Projective cover

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a category and X an object in C {\displaystyle {\mathcal {C}}} . A projective cover is a pair (P,p), with P a projective object in C {\displaystyle {\mathcal...

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Injective object

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the theory of model categories. The dual notion is that of a projective object. An object Q {\displaystyle Q} in a category C {\displaystyle \mathbf {C}...

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Projective identification

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Projective identification is a term introduced by Melanie Klein and then widely adopted in psychoanalytic psychotherapy. Projective identification may...

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Projection

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Look up projection, projecting, projective, or projector in Wiktionary, the free dictionary. Projection, projections or projective may refer to: Projection...

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Frank Zappa

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career. Zappa's output is unified by a conceptual continuity he termed "Project/Object", with numerous musical phrases, ideas, and characters reappearing across...

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Projective space

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concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...

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Projective geometry

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In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...

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Projective module

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Thus, by definition, projective modules are precisely the projective objects in the category of R-modules. A module P is projective if and only if every...

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Projective variety

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In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space P n {\displaystyle \mathbb {P}...

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Projective plane

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the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

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Free module

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properties free, projective, flat, and torsion-free are equivalent. See local ring, perfect ring and Dedekind ring. Free object Projective object free presentation...

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Projective

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variety Projective linear group Projective module Projective line Projective object Projective transformation Projective hierarchy Projective connection...

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The Crux of the Biscuit

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celebrate the 40th anniversary of his album Apostrophe ('). It is the fourth project in a series of 40th Anniversary FZ Audio Documentaries, following MOFO...

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Homography

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In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces...

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Object relations theory

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four functions that projective identification may serve. As in the traditional Kleinian model, it serves as a defense. Projective identification serves...

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Derived functor

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category A has enough projectives (i.e. for every object A of A there exists an epimorphism P → A where P is a projective object), then one can define...

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Apache Maven

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aforementioned tasks. A Project Object Model (POM) provides all the configuration for a single project. General configuration covers the project's name, its owner...

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Algebraic variety

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called a projective algebraic set if V = Z(S) for some S.: 9  An irreducible projective algebraic set is called a projective variety.: 10  Projective varieties...

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Category of sets

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is an injective object in Set. Every set is a projective object in Set (assuming the axiom of choice). The finitely presentable objects in Set are the...

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Derived category

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that A has enough projectives, i.e. for every object X there is an epimorphism from a projective object P to X, one can use projective resolutions instead...

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Axiom of choice

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free abelian group is projective. Baer's criterion: Every divisible abelian group is injective. Every set is a projective object in the category Set of...

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JSON

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JSON (JavaScript Object Notation, pronounced /ˈdʒeɪsən/ or /ˈdʒeɪˌsɒn/) is an open standard file format and data interchange format that uses human-readable...

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Homogeneous coordinates

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dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three...

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