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-morphism
-morphism (ˈmɔːfɪz(ə)m) terminal element [f. Gr. µορϕή form + -ism] of ns. with the sense ‘condition or property of having a (certain) form or character’, and in Math. ‘a transformation or correspondence of a (certain) kind’: e.g. heteromorphism, isomorphism. Oxford English Dictionary
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Morphism
In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformati... wikipedia.org
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algebraic geometry - Definition of proper morphism between schemes ...
The definition of proper morphism by separated, finite type, universally closed properties doesn't look enlightening to me. I am trying to look for a simpler characterization for this concept. As we know properness in algebraic geometry is the analog notion of compactness in topology. In topology the definition of the proper map is that the ...
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Proper morphism - Wikipedia
Proper morphism. In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces . Some authors call a proper variety over a field k a complete variety. For example, every projective variety over a field k is proper over k. A scheme X of finite type over the complex numbers (for example, a ...
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Zero morphism
In category theory, a branch of mathematics, a zero morphism is a special kind of morphism exhibiting properties like the morphisms to and from a zero object. Definitions Suppose C is a category, and f : X → Y is a morphism in C. The morphism f is called a constant morphism (or sometimes left zero m... wikipedia.org
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Proper morphism
In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces. Some authors call a proper variety over a field k a complete variety. For example, every projective variety over a field k is proper over k. A scheme X of finite type over the compl... wikipedia.org
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Flat morphism
In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., is a flat map for all P in X. A map of rings is called flat if it is a homomorphism that ... wikipedia.org
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Harmonic morphism
In mathematics, a harmonic morphism is a (smooth) map between Riemannian manifolds that pulls back real-valued harmonic functions on the codomain to harmonic functions on the domain. Harmonic morphisms form a special class of harmonic maps i.e. those that are horizontally (weakly) conformal. In loca... wikipedia.org
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Flat morphism - Wikipedia
Flat morphism. In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., is a flat map for all P in X. [1] A map of rings is called flat if it is a homomorphism that makes B a flat A -module.
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Normal morphism
In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism. A normal category is a category in which every monomorphism is normal. A conormal category is one in which every epimorphism is conormal. Definition ... wikipedia.org
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Radicial morphism
In algebraic geometry, a morphism of schemes f: X → Y is called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective. (EGA I, (3.5.4)) This is a generalization of the notion of a purely inseparable extension of fields (sometimes called a radicial extensio... wikipedia.org
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Étale morphism
In algebraic geometry, an étale morphism () is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but becau... wikipedia.org
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Finite morphism
In algebraic geometry, a finite morphism between two affine varieties is a dense regular map which induces isomorphic inclusion between their coordinate rings, such that is integral over . This definition can be extended to the quasi-projective varieties, such that a regular map between quasiproject... wikipedia.org
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Unramified morphism
In algebraic geometry, an unramified morphism is a morphism of schemes such that (a) it is locally of finite presentation and (b) for each and , we have that The residue field is a separable algebraic extension of . where and are maximal ideals of the local rings. A flat unramified morphism is calle... wikipedia.org
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Contraction morphism
In algebraic geometry, a contraction morphism is a surjective projective morphism between normal projective varieties (or projective schemes) such that or, equivalently, the geometric fibers are all connected (Zariski's connectedness theorem). It is also commonly called an algebraic fiber space, as ... wikipedia.org
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