Adjoint functors | Category theory
In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is a monoid in the category of endofunctors. An endofunctor is a functor mapping a category to itself, and a monad is an endofunctor together with two natural transformations required to fulfill certain coherence conditions. Monads are used in the theory of pairs of adjoint functors, and they generalize closure operators on partially ordered sets to arbitrary categories. Monads are also useful in the theory of datatypes and in functional programming languages, allowing languages with non-mutable states to do things such as simulate for-loops; see Monad (functional programming). (Wikipedia).
Category Theory 10.2: Monoid in the category of endofunctors
Monad as a monoid in the category of endofunctors
From playlist Category Theory
Category theory for JavaScript programmers #15: for comprehensions
http://jscategory.wordpress.com/source-code/ Note these are far more general than the current proposals for generators and iterators in "ES.next", the next version of JavaScript (whose standardized form is ECMAScript, thus "ES").
From playlist Category theory for JavaScript programmers
Category theory for JavaScript programmers #24: monoidal functors
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Category Theory 4.1: Terminal and initial objects
Terminal and initial objects
From playlist Category Theory
Category theory for JavaScript programmers #25: laziness and recursive datatypes
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Semantics of Higher Inductive Types - Michael Shulman
Semantics of Higher Inductive Types Michael Shulman University of California, San Diego; Member, School of Mathematics February 27, 2013
From playlist Mathematics
Category theory for JavaScript programmers #19: some formality around categories
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Steve Awodey: Type theories and polynomial monads
Abstract: A system of dependent type theory T gives rise to a natural transformation p : Terms → Types of presheaves on the category Ctx of contexts, termed a "natural model of T". This map p in turn determines a polynomial endofunctor P : Ctxˆ → Ctxˆ on the category of all presheaves. It
From playlist Topology
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
Shadows of Computation - Lecture 7 - Because it's there
Welcome to Shadows of Computation, an online course taught by Will Troiani and Billy Snikkers, covering the foundations of category theory and how it is used by computer scientists to abstract computing systems to reveal their intrinsic mathematical properties. In the seventh lecture Will
From playlist Shadows of Computation
Brian Beckman: Don't fear the Monad
Cross posted from msdn's channel 9. Functional programming is increasing in popularity these days given the inherent problems with shared mutable state that is rife in the imperative world. As we march on to a world of multi and many-core chipsets, software engineering must evolve to bett
From playlist Software Development Lectures
ZuriHac 2016: Monad Homomorphisms
A Google TechTalk, July 23, 2016, presented by Edward Kmett ABSTRACT: The way that we use the monad transformer library today leads to code that has pathological performance problems. Can we do better? https://wiki.haskell.org/ZuriHac2016
From playlist ZuriHac 2016
Okay but WTF is a MONAD?????? #SoME2
"A monad is a monoid in the category of endofunctors" Words dreamed up by the utterly insane!!! In this video I go over the common meme and explain it's origins and show many examples of monads out in the wild! This video is intended for anyone with programming experience who wants to fin
From playlist Summer of Math Exposition 2 videos
Category theory for JavaScript programmers #26: continuation passing monad
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Christopher TOWNSEND - There are categories of ‘spaces' that are not categories of locales
Abstract We described a short list of categorical axioms that make a category behave like the category of locales. In summary the axioms assert that the category has an object that behaves like the Sierpnski space and this object is double exponentiable. A number of the usual results of lo
From playlist Topos à l'IHES
Category theory for JavaScript programmers #14: monads as monoids
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory