functorial

1 9.9

Describing a change that keeps relationships between mathematical objects the same

adjective
/fʌŋˈtɔːrɪəl/

Specialized

: functorial

The concept of functorial mappings is essential in category theory.

Examples

A functorial construction preserves the relationships between mathematical objects.
The functorial approach simplifies many proofs in modern algebra.
Researchers discussed the functorial properties of the mapping in their seminar.
In mathematics, functorial relationships help to define structures.
The mathematician explained the concept of functorial relationships between different categories.
In category theory, a functorial mapping preserves the structure of the categories involved.
Understanding functorial properties is essential for advanced studies in mathematics.

Surface Forms

functorial positive

Morphology

functorial = functor (transparent) = functor + ial

The adjective is formed by adding the productive suffix '-ial' to the noun 'functor', yielding 'relating to a functor'; the relation is direct if the learner knows 'functor'.

Etymology

The word functorial comes from functor, which is like the common word function and goes back to an old word meaning 'to do' or 'perform'. The ending -ial means 'related to', so functorial describes something that is 'related to a functor'—in math this means a mapping that keeps the relationships between objects the same.