# functor

## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• n. One that performs an operation or a function.
• n. Grammar See function word.

• n. a function word
• n. a function object
• n. a structure-preserving mapping between categories: if F is a functor from category C to category D, then F maps objects of C to objects of D and morphisms of C to morphisms of D such that any morphism f:X→Y of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if then , and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.

## Etymologies

New Latin, from Latin fūnctiō, performance, function; see function.
(American Heritage® Dictionary of the English Language, Fourth Edition)

## Examples

• In the regimented environment of LeÅniewski's logical languages this always takes place in the following way: a combining expression, which we may call a functor, precedes a left parenthesis of some kind, which is then followed by a sequence of one or more argument expressions, followed by a right parenthesis symmetric to the other one, which terminates the complex.

StanisÅaw LeÅniewski

• Strict memoization (really hyper-strict) is centered on a family of trie functors, defined as a functor

• "functor" we need to be clear whether we're talking about one of these objects (ie a functor in the underlying category), or about a functor over this category.

• I am pretty sure that violates one of the applicative functor laws. (f pure x = pure (\$x) f).

Patterns in Haskell « Alex McLean

• So quantum mechanics and general relativity at least within this “partial functor” are equivalent, and might ultimately prove to be two aspects of an identical system.

If We Live in a Multiverse, How Many Are There? | Universe Today

• Since quotations are functor expressions without internal structure, (BQ2) is explained: there's no possibility for quantifying into a quotation on this view.

Quotation

• For example, “is” has s/nn as its categorial index; it says that” is “is a two-placed functor of two nominal arguments which forms a sentence.

Lvov-Warsaw School

• Moreover, in GEM the generalized Product principle (P. 16Ï) is also derivable as a theorem, with ˜Ï™ as weak as the requirement of mutual overlap, and we can introduce a corresponding functor as follows:

Wild Dreams Of Reality, 3

• Coarse-graining might be represented as a functor, or something like that, establishing some kind of equivalence which lets you have a weaker notion of isomorphism.

Arrow of Time FAQ

• With Protothetic launched, LeÅniewski could now look back on his system of foundations and see that it consisted of a hierarchy of three systems, developed in reverse order: Protothetic, introducing connectives, quantifiers and higher functions; Ontology, introducing the new category of names, with the new primitive ˜is™, and Mereology, based on a primitive mereological functor such as

StanisÅaw LeÅniewski

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