different between functor vs closure

English

Etymology

From function, modeled after factor.

Pronunciation

• (Received Pronunciation) IPA^(key): /?f??kt?/

Noun

functor (plural functors)

1. (grammar) A function word.
2. (object-oriented programming) A function object.
3. (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

   • 1991, Natalie Wadhwa (translator), Yu. A. Brudny?, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, Volume I, Elsevier (North-Holland), page 143,

     Choosing for ${\displaystyle U}$ the operation of closure, regularization or relative completion, we obtain from a given functor ${\displaystyle {\mathcal {F}}\in {\mathcal {JF}}}$ the functors

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

   • 2004, William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, Jeffrey H. Smith, Homotopy Limit Functors on Model Categories and Homotopical Categories, American Mathematical Society, page 165,

     Given a homotopical category ${\displaystyle X}$ and a functor ${\displaystyle u:A\rightarrow B}$, a homotopical ${\displaystyle u}$-colimit (resp. ${\displaystyle u}$-limit) functor on ${\displaystyle X}$ will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor ${\displaystyle X^{u}:X^{B}\rightarrow X^{A}}$ (47.1).

   • 2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,

     In this chapter, we recall the definition of the category of ${\displaystyle \Sigma _{*}}$-objects and we review the relationship between ${\displaystyle \Sigma _{*}}$-objects and functors. In short, a ${\displaystyle \Sigma _{*}}$-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor ${\displaystyle S(M):X\rightarrow S(M,X)}$, defined by a formula of the form

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

4. (functional programming) A structure allowing a function to apply within a generic type, in a way conceptually similar to a functor in category theory.

Derived terms

• contravariant functor
• functor category
• representable functor

Translations

Further reading

• function word on Wikipedia.Wikipedia
• functor on Wikipedia.Wikipedia
• functor (functional programming) on Wikipedia.Wikipedia
• “functor”, in Lexico, Dictionary.com; Oxford University Press, 2019–present.

Portuguese

Alternative forms

• funtor

Noun

functor m (plural functores)

1. (category theory) functor (a mapping between categories)

English

Etymology

From Middle English closure, from Old French closure, from Late Latin clausura, from Latin claudere (“to close”); see clausure and cloture (etymological doublets) and close.

Pronunciation

• enPR: kl?'zhûr
  • (UK) IPA^(key): /?kl??.??(?)/
  • (US) IPA^(key): /?klo?.??/, /?klo?.??/

Noun

closure (countable and uncountable, plural closures)

1. An event or occurrence that signifies an ending.
2. A feeling of completeness; the experience of an emotional conclusion, usually to a difficult period.
3. A device to facilitate temporary and repeatable opening and closing.
4. (programming) An abstraction that represents a function within an environment, a context consisting of the variables that are both bound at a particular time during the execution of the program and that are within the function's scope.
5. (mathematics) The smallest set that both includes a given subset and possesses some given property.
6. (topology, of a set) The smallest closed set which contains the given set.
   • 1955 [Van Nostrand Reinhold], John L. Kelley, General Topology, 2017, Dover, page 42,

     The closure (${\displaystyle {\mathfrak {T}}}$-closure) of a subset A of a topological space ${\displaystyle (X,{\mathfrak {T}})}$ is the intersection of the members of the family of all closed sets containing A. […]

     7 THEOREM The closure of any set is the union of the set and the set of its accumulation points.

7. The act of shutting; a closing.

   the closure of a door, or of a chink

8. That which closes or shuts; that by which separate parts are fastened or closed.
   • 1729 November 28, Alexander Pope, Letter to Jonathan Swift, 1824, The Works of Jonathan Swift: Containing Additional Letters, Volume 17, 2nd Edition, page 284,

     I admire on this consideration your sending your last to me quite open, without a seal, wafer, or any closure whatever, manifesting the utter openness of the writer.

9. (obsolete) That which encloses or confines; an enclosure.
   • c. 1593, William Shakespeare Richard III, Act 3, Scene 3, 1765, Samuel Johnson, George Steevens (editors) The Plays of William Shakespeare, Volume XI, 1808, page 97,

     O thou bloody prison […] / Within the guilty closure of thy walls / Richard the Second here was hacked to death.

10. (politics) A method of ending a parliamentary debate and securing an immediate vote upon a measure before a legislative body.
11. (sociology) The phenomenon by which a group maintains its resources by the exclusion of others from their group based on varied criteria. ^Wp
12. The process whereby the reader of a comic book infers the sequence of events by looking at the picture panels.
    • 2009, Randy Duncan, Matthew J. Smith, The Power of Comics: History, Form and Culture (page 166)

      The comic book reader performs closure within each panel, between panels, and among panels.

Hyponyms

• (computing): function closure, lexical closure
• (device): clasp, hasp, latch, hook and eye

Troponyms

• (computer science) thunk

Derived terms

• closure operator
• closure space

Translations

See also

• cloture

References

• closure on Wikipedia.Wikipedia

Anagrams

• Clouser, colures