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- Categorical_quotient abstract "In algebraic geometry, given a category C, a categorical quotient of an object X with action of a group G is a morphism that(i) is invariant; i.e., where is the given group action and p2 is the projection.(ii) satisfies the universal property: any morphism satisfying (i) uniquely factors through .One of the main motivations for the development of geometric invariant theory was the construction of a categorical quotient for varieties or schemes.Note need not be surjective. Also, if it exists, a categorical quotient is unique up to a canonical isomorphism. In practice, one takes C to be the category of varieties or the cateogy of schemes over a fixed scheme. A categorical quotient is a universal categorical quotient if it is stable under base change: for any , is a categorical quotient.A basic result is that geometric quotients (e.g., ) and GIT quotients (e.g., ) are categorical quotients.".
- Categorical_quotient wikiPageID "39561038".
- Categorical_quotient wikiPageRevisionID "600734863".
- Categorical_quotient subject Category:Algebraic_geometry.
- Categorical_quotient comment "In algebraic geometry, given a category C, a categorical quotient of an object X with action of a group G is a morphism that(i) is invariant; i.e., where is the given group action and p2 is the projection.(ii) satisfies the universal property: any morphism satisfying (i) uniquely factors through .One of the main motivations for the development of geometric invariant theory was the construction of a categorical quotient for varieties or schemes.Note need not be surjective.".
- Categorical_quotient label "Categorical quotient".
- Categorical_quotient sameAs m.0vxcr4g.
- Categorical_quotient sameAs Q17097821.
- Categorical_quotient sameAs Q17097821.
- Categorical_quotient wasDerivedFrom Categorical_quotient?oldid=600734863.
- Categorical_quotient isPrimaryTopicOf Categorical_quotient.