functorial morphism - définition. Qu'est-ce que functorial morphism
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Qu'est-ce (qui) est functorial morphism - définition

TRANSFORMATION BETWEEN TWO FUNCTORS STUDIED IN CATEGORY THEORY
Natural (category theory); Natural equivalence; Natural isomorphism; Naturally isomorphic; Natural transformations; Infranatural transformation; Natural homomorphism; Natural operation; Natural operations; Natural Transformation; Naturality; Unnatural isomorphism; Identity natural transformation
  • This is the commutative diagram which is part of the definition of a natural transformation between two functors.
  • Horizontal and vertical composition of natural transformations

Naturality         
·noun Nature; naturalness.
Natural transformation         
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e.
Morphism of schemes         
RINGED SPACE MORPHISM BETWEEN SCHEMES; LOCALLY A COMMUTATIVE RING HOMOMORPHISM BETWEEN COORDINATE RINGS
Scheme morphism; Graph morphism (algebraic geometry)
In algebraic geometry, a morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by definition, a morphism in the category of schemes.

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Natural transformation

In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Informally, the notion of a natural transformation states that a particular map between functors can be done consistently over an entire category.

Indeed, this intuition can be formalized to define so-called functor categories. Natural transformations are, after categories and functors, one of the most fundamental notions of category theory and consequently appear in the majority of its applications.