In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) 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 all areas within mathematics to which category theory is applied. The words category and functor were borrowed by mathematicians from the philosophers Aristotle and Rudolf Carnap, respectively. The latter used functor in a linguistic context;see function word. (Wikipedia).
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From playlist Your Career
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From playlist Machine Learning
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From playlist Career Examples
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From playlist Photoshop
Clojure - the Reader and Evaluator (4/4)
Part of a series teaching the Clojure language. For other programming topics, visit http://codeschool.org
From playlist the Clojure language
Clojure - the Reader and Evaluator (2/4)
Part of a series teaching the Clojure language. For other programming topics, visit http://codeschool.org
From playlist the Clojure language
Introduction to the C programming language. Part of a larger series teaching programming. See http://codeschool.org
From playlist The C language
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From playlist How To Be Creative
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From playlist Networking
Higher Algebra 6: Derived Functors
In this video, we define and discuss derived functors between derived categories of abelian categories. Additionally we discuss the notion of adjoint functors and Kan extensions. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.
From playlist Higher Algebra
Teena Gerhardt - 3/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Serge Bouc: Correspondence functors
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Yonatan Harpaz - New perspectives in hermitian K-theory II
Warning: around 32:30 in the video, in the slide entitled "Karoubi's conjecture", a small mistake was made - in the third bulleted item the genuine quadratic structure appearing should be the genuine symmetric one (so both the green and red instances of the superscript gq should be gs), an
From playlist New perspectives on K- and L-theory
This lecture is part of an online course on category theory. We define adoint functors and give severalexamples of them. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj51F9XZ_Ka4bLnQoxTdMx0AL
From playlist Categories for the idle mathematician
PROG2006: Haskell - Folds, Functor, Applicative, Mondas
PROG2006 Advanced Programming Haskell Review: Lists, Folds, Applicative Functor, Functor Intro to Monads
From playlist PROG2006 - Programming
This lecture is part of an online course on categories. Any object of a category can be thought of as a representable functor in the category of presheaves. We give several examples of representable functors. Then we state Yoneda's lemma, which roughly that morphisms of objects are he sa
From playlist Categories for the idle mathematician
ITHT: Part 10- Derived Functors
Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#DerivedFunctors Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub... Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name:
From playlist Introduction to Homotopy Theory
LambdaConf 2015 - Give me Freedom or Forgeddaboutit Joseph Abrahamson
The Haskell community is often abuzz about free monads and if you stick around for long enough you'll also see notions of free monoids, free functors, yoneda/coyoneda, free seminearrings, etc. Clearly "freedom" is a larger concept than just Free f a ~ f (Free f) + a. This talk explores bri
From playlist LambdaConf 2015
Introduction to the C programming language. Part of a larger series teaching programming. See http://codeschool.org
From playlist The C language