Synoniemen & Informatie over | Engels woord MORPHISM

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Voorbeelden van het gebruik van MORPHISM in een zin

• Quasi-compact morphism, a morphism of schemes for which the inverse image of any quasi-compact open set is again quasi-compact.
• In the more general setting of category theory, a monomorphism (also called a monic morphism or a mono) is a left-cancellative morphism.
• In category theory, an epimorphism is a morphism f : X → Y that is right-cancellative in the sense that, for all objects Z and all morphisms ,.
• An exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category) such that the image of one morphism equals the kernel of the next.
• Intuitively, the kernel of the morphism f : X → Y is the "most general" morphism k : K → X that yields zero when composed with (followed by) f.
• In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism.
• The functor U is to be thought of as a forgetful functor, which assigns to every object of C its "underlying set", and to every morphism in C its "underlying function".
• If G and H are two partially ordered groups, a map from G to H is a morphism of partially ordered groups if it is both a group homomorphism and a monotonic function.
• A cogenerator is an object C such that for every nonzero object H there exists a nonzero morphism f: H → C.
• An equivalent algebraic approach starts from the observation that a supermanifold is determined by its ring of supercommutative smooth functions, and that a morphism of supermanifolds corresponds one to one with an algebra homomorphism between their functions in the opposite direction, i.
• Monro (1987) investigated the category Mul of multisets and their morphisms, defining a multiset as a set with an equivalence relation between elements "of the same sort", and a morphism between multisets as a function that respects sorts.
• In any universal algebraic category, including the categories where difference kernels are used, as well as the category of sets itself, the object E can always be taken to be the ordinary notion of equaliser, and the morphism eq can in that case be taken to be the inclusion function of E as a subset of X.
• A morphism of distributive lattices is just a lattice homomorphism as given in the article on lattices, i.
• The morphism f is called a constant morphism (or sometimes left zero morphism) if for any object W in C and any , fg = fh.
• In particular, one can replace the extension of fields by any morphism of ringed topoi, and the hypotheses on X can be weakened to e.
• Typically, this happens because a birational morphism contracts some subvarieties of X to points in Y.
• In categories with zero morphisms, one can define a cokernel of a morphism f as the coequalizer of f and the parallel zero morphism.
• A functor F : C → D yields an isomorphism of categories if and only if it is bijective on objects and on morphism sets.
• An isogeny between algebraic groups is a surjective morphism with finite kernel; two tori are said to be isogenous if there exists an isogeny from the first to the second.
• Since the detailed structure of objects is immaterial in category theory, the definition of subobject relies on a morphism that describes how one object sits inside another, rather than relying on the use of elements.
• The concept of étale morphism (and so étale cohomology) depends on the flat morphism concept: an étale morphism being flat, of finite type, and unramified.
• On the other hand, the direct image of a coherent sheaf under a proper morphism is coherent, by results of Grauert and Grothendieck.
• This had been shown by Grothendieck if the morphism f: X → Y is locally of finite presentation, which follows from the other assumptions if Y is noetherian.
• For example, for the minimal genus 1 fibration of a (quasi)-bielliptic surface induced by the Albanese morphism, the canonical bundle formula gives that this fibration has no multiple fibers.
• More generally, complexification is an example of extension of scalars – here extending scalars from the real numbers to the complex numbers – which can be done for any field extension, or indeed for any morphism of rings.

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