branch of mathematics, a zero morphism is a special kind of morphism exhibiting properties like the morphisms to and from a zero object. Suppose C is a...

zero morphism in a category is a generalised absorbing element under function composition: any morphism composed with a zero morphism gives a zero morphism...

called a zero object or null object. A pointed category is one with a zero object. A strict initial object I is one for which every morphism into I is...

other of morphisms. There are two objects that are associated to every morphism, the source and the target. A morphism f from X to Y is a morphism with source...

algebra. 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. Note...

(linguistics) Null allomorph Zero (linguistics) Disfix "Lexicon of Linguistics". lexicon.hum.uu.nl. Retrieved 2019-12-05. "Zero Morph". Glossary of Linguistic...

has a zero element 0. This is the zero morphism from A to B. Because composition of morphisms is bilinear, the composition of a zero morphism and any...

as A → C → I → B, where the morphism on the left is the coimage, the morphism on the right is the image, and the morphism in the middle (called the parallel...

language. For an example, see Standard Chinese phonology#Zero onset. In morphology, a zero morph, consisting of no phonetic form, is an allomorph of a morpheme...

for zero manifold Several terms related to 0 (number) Zero map, see constant function Zero morphism, a kind of morphism in category theory Zero matrix...

which means that a morphism A → {0} must exist and be unique for an arbitrary object A. This morphism maps any element of A to 0. The zero object, also by...

question must have zero morphisms. The cokernel of a morphism f : X → Y is defined as the coequalizer of f and the zero morphism 0XY : X → Y. Explicitly...

respectively. The morphism f is determined by its values on the letters of B and conversely any map from B to M extends to a morphism. A morphism is non-erasing...

the idea of a zero object, often denoted 0, and the related concept of zero morphisms, which generalize the zero function. The value zero plays a special...

factorization u {\displaystyle u} . The morphism u {\displaystyle u} is sometimes called the mediating morphism. Limits are also referred to as universal...

In categories with zero morphisms, one can define a cokernel of a morphism f as the coequalizer of f and the parallel zero morphism. In preadditive categories...

morphism is a monomorphism. This follows from the fact that the only ideals in a field F are the zero ideal and F itself. One can then view morphisms...

abelian. Specifically: AB1) Every morphism has a kernel and a cokernel. AB2) For every morphism f, the canonical morphism from coim f to im f is an isomorphism...

{\displaystyle A_{k},} and p l ∘ i k = 0 {\textstyle p_{l}\circ i_{k}=0} , the zero morphism A k → A l , {\displaystyle A_{k}\to A_{l},} for k ≠ l , {\displaystyle...

In algebraic geometry, an unramified morphism is a morphism f : X → Y {\displaystyle f:X\to Y} of schemes such that (a) it is locally of finite presentation...

will denote the projection morphisms, and ik will denote the injection morphisms. The diagonal morphism is the canonical morphism ∆: A → A ⊕ A, induced by...

object Zero object Subobject Group object Magma object Natural number object Exponential object Epimorphism Monomorphism Zero morphism Normal morphism Dual...

{\displaystyle \ker(f)=M} , meaning that f {\displaystyle f} is the zero morphism, or that ker ⁡ ( f ) = 0 {\displaystyle \ker(f)=0} , meaning that f...

naturally the structure of a locally ringed space; a morphism between algebraic varieties is precisely a morphism of the underlying locally ringed spaces. If X...

particular morphism. There is no longer any notion of an identity morphism, nor of a particular composition of two morphisms. Instead, morphisms from the...

_{S}^{n}\to S} where g is étale. A morphism of finite type is étale if and only if it is smooth and quasi-finite. A smooth morphism is stable under base change...

In algebraic geometry, an étale morphism (French: [etal]) is a morphism of schemes that is formally étale and locally of finite presentation. This is...

addition is defined from pointwise addition in M {\displaystyle M} . The zero morphism and the identity are the respective neutral elements. If M = R n {\displaystyle...

In algebraic geometry, given a morphism of schemes p : X → S {\displaystyle p:X\to S} , the diagonal morphism δ : X → X × S X {\displaystyle \delta :X\to...

mathematics, in particular 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...