morphism's Usage Examples:

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.

universal property is an important property which is satisfied by a universal morphism (see Formal Definition).

Universal morphisms can also be thought of more.

Several terms used in category theory, including the term "morphism", are used differently from their uses in the rest of mathematics.

on sheaves yield a geometric morphism between the associated topoi.

A point of a topos X is defined as a geometric morphism from the topos of sets to X.

a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism.

object I in C such that for every object X in C, there exists precisely one morphism I → X.

object x, there exists a morphism 1x : x → x (some authors write idx) called the identity morphism for x, such that every morphism f : a → x satisfies 1x.

category theory, a monomorphism (also called a monic morphism or a mono) is a left-cancellative morphism.

A morphism of magmas is a function, f : M → N, mapping magma M to magma N, that preserves.

category theory, an epimorphism (also called an epic morphism or, colloquially, an epi) is a morphism f : X → Y that is right-cancellative in the sense that.

In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G.

the Frobenius morphism for a scheme.

The most fundamental is the absolute Frobenius morphism.

However, the absolute Frobenius morphism behaves poorly.

product of a family of objects is the "most general" object which admits a morphism to each of the given objects.

Biomorphism models artistic design elements on naturally occurring patterns or shapes reminiscent of nature and living organisms.

between Hilbert spaces) is an object Q and a morphism q : Y → Q such that the composition q f is the zero morphism of the category, and furthermore q is universal.

trivial) cofibration (or sometimes called an anodyne morphism).

Axioms Retracts: if g is a morphism belonging to one of the distinguished classes, and f.

Given any morphism f between objects X and Y, if there is an inclusion map into the domain.

Intuitively, the kernel of the morphism f : X → Y is the "most general" morphism k : K → X that yields zero when composed with (followed.

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.