(in mathematics) a function that maps elements of one set to those of another
Examples of 'functor' in a sentence
functor
This functor expresses the relation between algebras and carrier-sets.
Viliam Slodičák 2011, 'Some useful structures for categorical approach for program behavior', Journal of Information and Organizational Scienceshttp://jios.foi.hr/index.php/jios/article/view/187. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this paper we introduce a notion of projectively inductively closed functor (p.i.c.-functor).
T.F. Zhuraev 2002, 'On paracompact spaces and projectively inductively closed functors', Applied General Topologyhttp://polipapers.upv.es/index.php/AGT/article/view/2110. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Additionally, we phrase mass-action kinetics as a functor on reaction networks with variable rates.
Manoj Gopalkrishnan, Ezra Miller, Anne Shiu 2013, 'A Projection Argument for Differential Inclusions, with Applications to Persistenceof Mass-Action Kinetics', Symmetry, Integrability and Geometry: Methods and Applicationshttp://dx.doi.org/10.3842/SIGMA.2013.025. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We give sufficient conditions for a functor to be a p.i.c.-functor.
T.F. Zhuraev 2002, 'On paracompact spaces and projectively inductively closed functors', Applied General Topologyhttp://polipapers.upv.es/index.php/AGT/article/view/2110. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We then define a semantical functor from the connector to the port automata category which preserves this composition.
Christian Krause 2009, 'Integrated Structure and Semantics for Reo Connectors and Petri Nets', Electronic Proceedings in Theoretical Computer Sciencehttp://arxiv.org/pdf/0911.5447v1. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The second one treats negation as a contravariant functor and the third one captures negation as adjointness.
Skowron Bartłomiej, Kubiś Wiesław 2018, 'Negating as turning upside down', Studies in Logic, Grammar and Rhetorichttp://www.degruyter.com/view/j/slgr.2018.54.issue-1/slgr-2018-0020/slgr-2018-0020.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure.
Danel Ahman, Tarmo Uustalu 2016, 'Directed Containers as Categories', Electronic Proceedings in Theoretical Computer Sciencehttp://arxiv.org/pdf/1604.01187v1. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The correspondence defines a contravariant functor from the category of topological groups to the categoryof complete lattices.
Wei He, Zhiqiang Xiao 2019, 'Lattice of compactifications of a topological group', Categories and General Algebraic Structures with Applicationshttp://www.cgasa.ir/article_61406_5c0d76f764a8ff7460747ef9016d1a97.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We construct a new category with a self-dual functor acting on it, which extends that duality.
Florin F. Nichita, Bartosz Zielinski 2012, 'The Duality between Corings and Ring Extensions', Axiomshttp://www.mdpi.com/2075-1680/1/2/173. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)