FUNCTOR

Etymology

Noun

functor (plural functors)

(grammar) A function word.

(object-oriented programming) A function object.

(category theory) A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows, in such a way as to preserve domains and codomains (of the arrows) as well as composition and identities.

Hyponym: endofunctor

In the category of categories, $\backslash (\backslash mathbb\{CAT\}\backslash )$, the objects are categories and the morphisms are functors.

$\backslash (\backslash overline\{F\}\; :\; \backslash overrightarrow\{X\}\; \backslash rightarrow\; \backslash overline\{F(\backslash overrightarrow\{X\})\},\; F^0\; :\; \backslash overrightarrow\{X\}\backslash rightarrow\; F(\backslash overrightarrow\{X\})^0,\; F^c\; :\; \backslash overrightarrow\{X\}\; \backslash rightarrow\; F(\backslash overrightarrow\{X\})^c\backslash )$.

$\backslash (S(M,X)\; =\; \backslash bigoplus^\backslash infty\_\{r=0\}\; \backslash left\; (\; M(r)\backslash otimes\; X^\{\backslash otimes\; r\}\backslash right\; )\_\{\backslash Sigma\_r\}\backslash )$.

Source: Wiktionary

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