functor (Q1347): Difference between revisions

@@ Property / subclass of @@
+function
@@ Property / subclass of: function / rank @@
+Normal rank
@@ Property / topic's main category @@
+Category:Functors
@@ Property / topic's main category: Category:Functors / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/02yzn
@@ Property / Freebase ID: /m/02yzn / rank @@
+Normal rank
@@ Property / Freebase ID: /m/02yzn / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / discoverer or inventor @@
+Samuel Eilenberg
@@ Property / discoverer or inventor: Samuel Eilenberg / rank @@
+Normal rank
@@ Property / discoverer or inventor: Samuel Eilenberg / qualifier @@
+point in time: 1942Timestamp +1942-00-00T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 year
Before 0
After 0
-Timestamp
++1942-00-00T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+year
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@@ Property / discoverer or inventor: Samuel Eilenberg / reference @@
+stated in: History of Homological Algebra
@@ Property / discoverer or inventor @@
+Saunders Mac Lane
@@ Property / discoverer or inventor: Saunders Mac Lane / rank @@
+Normal rank
@@ Property / discoverer or inventor: Saunders Mac Lane / qualifier @@
+point in time: 1942Timestamp +1942-00-00T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 year
Before 0
After 0
-Timestamp
++1942-00-00T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+year
 Before
 After
@@ Property / discoverer or inventor: Saunders Mac Lane / reference @@
+stated in: History of Homological Algebra
@@ Property / Commons category @@
+Functors
@@ Property / Commons category: Functors / rank @@
+Normal rank
@@ Property / Commons category: Functors / reference @@
+imported from Wikimedia project: English Wikipedia
@@ Property / Quora topic ID @@
+Functor-1
@@ Property / Quora topic ID: Functor-1 / rank @@
+Normal rank
@@ Property / Quora topic ID: Functor-1 / reference @@
+stated in: Quora
@@ Property / JSTOR topic ID @@
+functors
@@ Property / JSTOR topic ID: functors / rank @@
+Normal rank
@@ Property / part of @@
+category theory
@@ Property / part of: category theory / rank @@
+Normal rank
@@ Property / PSH ID @@
@@ Property / PSH ID: 7364 / rank @@
+Normal rank
@@ Property / nLab ID @@
+functor
@@ Property / nLab ID: functor / rank @@
+Normal rank
@@ Property / nLab ID: functor / reference @@
+imported from Wikimedia project: English Wikipedia
@@ Property / Encyclopædia Britannica Online ID @@
+topic/functor
@@ Property / Encyclopædia Britannica Online ID: topic/functor / rank @@
+Normal rank
@@ Property / Encyclopædia Britannica Online ID: topic/functor / qualifier @@
+subject named as: functor
@@ Property / OmegaWiki Defined Meaning @@
@@ Property / OmegaWiki Defined Meaning: 955376 / rank @@
+Normal rank
@@ Property / studied in @@
+category theory
@@ Property / studied in: category theory / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+156772000
@@ Property / Microsoft Academic ID: 156772000 / rank @@
+Normal rank
@@ Property / properties for this type @@
+definition domain
@@ Property / properties for this type: definition domain / rank @@
+Normal rank
@@ Property / properties for this type: definition domain / qualifier @@
+instance of: category
@@ Property / properties for this type @@
+codomain
@@ Property / properties for this type: codomain / rank @@
+Normal rank
@@ Property / properties for this type: codomain / qualifier @@
+instance of: category
@@ Property / KBpedia ID @@
+Functor
@@ Property / KBpedia ID: Functor / rank @@
+Normal rank
@@ Property / KBpedia ID: Functor / reference @@
+stated in: KBpedia
retrieved: 9 July 2020Timestamp +2020-07-09T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2020-07-09T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / different from @@
+function object
@@ Property / different from: function object / rank @@
+Normal rank
@@ Property / different from: function object / qualifier @@
+subject named as: functor
@@ Property / Encyclopedia of Mathematics article ID @@
+Functor
@@ Property / Encyclopedia of Mathematics article ID: Functor / rank @@
+Normal rank
@@ Property / MathWorld ID @@
+Functor
@@ Property / MathWorld ID: Functor / rank @@
+Normal rank
@@ Property / defining formula @@
+ ${\begin{aligned}F(\operatorname {id} _{X})&=\operatorname {id} _{F(X)}\\F(f\circ g)&=Ff\circ Fg\end{aligned}}$ 
\begin{aligned}F(\operatorname{id}_X)&=\operatorname{id}_{F(X)}\\F(f\circ g)&=Ff\circ Fg\end{aligned}
+Normal rank
@@ Property / OpenAlex ID @@
+C156772000
@@ Property / OpenAlex ID: C156772000 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C156772000 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / in defining formula @@
+ $F$ 
F
@@ Property / in defining formula: $F$ / rank @@
+Normal rank
@@ Property / in defining formula: $F$ / qualifier @@
+symbol represents: functor
@@ Property / in defining formula @@
+ $\operatorname {id}$ 
\operatorname{id}
@@ Property / in defining formula: $\operatorname {id}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\operatorname {id}$ / qualifier @@
+symbol represents: identity function
@@ Property / in defining formula @@
+ $f\circ g$ 
f\circ g
@@ Property / in defining formula: $f\circ g$ / rank @@
+Normal rank
@@ Property / in defining formula: $f\circ g$ / qualifier @@
+symbol represents: function composition
@@ Property / ScienceDirect topic ID @@
+mathematics/functor
@@ Property / ScienceDirect topic ID: mathematics/functor / rank @@
+Normal rank
@@ Property / ProofWiki ID @@
+Definition:Functor
@@ Property / ProofWiki ID: Definition:Functor / rank @@
+Normal rank
@@ Property / Treccani ID @@
+funtore
@@ Property / Treccani ID: funtore / rank @@
+Normal rank
@@ Property / Treccani ID: funtore / qualifier @@
+subject named as: funtore
@@ Property / Metamath statement ID @@
+df-func
@@ Property / Metamath statement ID: df-func / rank @@
+Normal rank

Latest revision as of 15:57, 29 July 2024

in category theory, a mapping between categories that preserves their structure (identity morphisms, composition of morphisms)

covariant functor
contravariant functor

Language	Label	Description	Also known as
English	functor	in category theory, a mapping between categories that preserves their structure (identity morphisms, composition of morphisms)	covariant functor contravariant functor