Everything about Functor
Mapping between categories
In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces. Nowadays, functors are used throughout modern mathematics to relate various categories. Thus, functors are important in every area of mathematics where category theory is applied. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: FunctorA 5-minute orientation
- Skim a recent paper: The six-functor formalism for rigid analytic motivesInfluential work since 2022
- Pick up a classic book: CategoriesThe most-reprinted book on the subject
- Read the landmark paper: A Modular Functor Which is Universal¶for Quantum ComputationCited 382 times
- Go sideways: Representable functorA closely related topic
- Go sideways: Yoneda lemmaA closely related topic
📖 Definitions
Noun A function word.
Noun A function object.
Noun A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities.
Noun A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A Modular Functor Which is Universal¶for Quantum Computation
The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor
THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
A functor-valued invariant of tangles
The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces
A class ofC *-algebras and topological markov chains II: Reducible chains and the ext-functor forC *-algebras
Frequency and form as determinants of functor sensitivity in English-acquiring infants
Leray functor and cohomological Conley index for discrete dynamical systems
🆕 Influential since 2022
📚 Books worth reading
CategoriesHorst Schubert · 1972
Functor analysis of natural languageJohn Lehrberger · 1974
Functorial Model TheoryCyrus F. Nourani · 2016
Kategorien und FunktorenBodo Pareigis · 1969
Sets, sequences, and mappingsKenneth W. Anderson · 1963- 📕Combinatorial FunctorsJ. N. Crossley, A. Nerode · 1973
Kan extensions in enriched category theoryEduardo J. Dubuc · 1970
Functorial knot theoryDavid N. Yetter · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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