Functors | Algebraic topology

Calculus of functors

In algebraic topology, a branch of mathematics, the calculus of functors or Goodwillie calculus is a technique for studying functors by approximating them by a sequence of simpler functors; it generalizes the sheafification of a presheaf. This sequence of approximations is formally similar to the Taylor series of a smooth function, hence the term "calculus of functors". Many objects of central interest in algebraic topology can be seen as functors, which are difficult to analyze directly, so the idea is to replace them with simpler functors which are sufficiently good approximations for certain purposes.The calculus of functors was developed by Thomas Goodwillie in a series of three papers in the 1990s and 2000s, and has since been expanded and applied in a number of areas. (Wikipedia).

Video thumbnail

Categories 2: Functors

This lecture is part of an online course on category theory. We define functors and give some examples 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

Video thumbnail

Calculus: Graphical Limits

In this video, we investigate how to compute limits of a function that is given graphically.

From playlist Calculus

Video thumbnail

Categories 4 Adjoint functors

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

Video thumbnail

Calculus 1 Lecture 3.1: Increasing/Decreasing and Concavity of Functions

Calculus 1 Lecture 3.1: Discussion of Increasing and Decreasing Intervals. Discussion of Concavity of functions.

From playlist Calculus 1 (Full Length Videos)

Video thumbnail

Calculus 1 Lecture 5.1: Finding Area Between Two Curves

Calculus 1 Lecture 5.1: Finding Area Between Two Curves

From playlist Calculus 1 (Full Length Videos)

Video thumbnail

Infinite Limits With Equal Exponents (Calculus)

#Calculus #Math #Engineering #tiktok #NicholasGKK #shorts

From playlist Calculus

Video thumbnail

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

Video thumbnail

Lecture 1: Invitation to topos theory

This talk introduces the motivating question for this semester of the Curry-Howard seminar, which is how to organise mathematical knowledge using topoi. The approach sketched out in the talk is via first-order theories, their associated classifying topoi, and adjoint pairs of functors betw

From playlist Topos theory seminar

Video thumbnail

Substructural Type Theory - Zeilberger

Noam Zeilberger IMDEA Software Institute; Member, School of Mathematics March 22, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Gregory Arone: Calculus of functors and homotopy theory (Lecture 2)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Seminar on Functor Calculus and Chromatic Methods" Abstract: The derivatives of a functor have a bimodule structure over a certain operad. If the Tate homology of the derivatives vanish, then

From playlist HIM Lectures: Junior Trimester Program "Topology"

Video thumbnail

Paul André Melliès - Dialogue Games and Logical Proofs in String Diagrams

After a short introduction to the functorial approach to logical proofs and programs initiated by Lambek in the late 1960s, based on the notion of free cartesian closed category, we will describe a recent convergence with the notion of ribbon category introduced in 1990 by Reshetikhin and

From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020

Video thumbnail

jQuery Conference SF 2012 Faster jQuery With Category Theory by John Bender

Math: It's certainly not something you expect to see at a conference about JavaScript, but even this far from its ivory towers it has an important role to play. Together we'll build two categories, see how satisfying the Functor laws shines light on a simple optimization for our jQuery met

From playlist jQuery Conference 2012 - San Francisco

Video thumbnail

Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups - Sam Nariman

Workshop on the h-principle and beyond Topic: Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups Speaker: Sam Nariman Affiliation: Purdue University Date: November 1, 2021 Abstract: I will discuss a remarkable generalization of Mather’s theorem by Thurston

From playlist Mathematics

Video thumbnail

Gregory Arone: Calculus of functors and homotopy theory (Lecture 3)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Seminar on Functor Calculus and Chromatic Methods" We will survey how many results about the Goodwillie tower of the identity functor have analogues for the Taylor tower of the functor V → BU(

From playlist HIM Lectures: Junior Trimester Program "Topology"

Video thumbnail

On Voevodsky's univalence principle - André Joyal

Vladimir Voevodsky Memorial Conference Topic: On Voevodsky's univalence principle Speaker: André Joyal Affiliation: Université du Québec á Montréal Date: September 11, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

MathZero, The Classification Problem, and Set-Theoretic Type Theory - David McAllester

Seminar on Theoretical Machine Learning Topic: MathZero, The Classification Problem, and Set-Theoretic Type Theory Speaker: David McAllester Affiliation: Toyota Technological Institute at Chicago Date: May 14, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Calculus 1 Lecture 5.4 Part 6

Calculus 1 Lecture 5.4 Part 6: Finding the Length of a Curve and The Surface Area of a Solid of Revolution.

From playlist Calculus 1 Playlist 2

Video thumbnail

Nicolas Behr - Categorification of Rule Algebras

Reporting on joint work in progress with P.-A. Melliès and N. Zeilberger, I will present a novel approach to formalize operations in compositional rewriting sys- tems wherein the number of ways to apply a rewrite is of interest. The approach is based upon defining a suitable double categor

From playlist Combinatorics and Arithmetic for Physics: Special Days 2022

Video thumbnail

Calculus 1 Lecture 5.4: Finding the Length of a Curve on a Plane

Calculus 1 Lecture 5.4: Finding the Length of a Curve on a Plane

From playlist Calculus 1 (Full Length Videos)

Related pages

Geometric topology | Functor | Manifold | Excision theorem | Mathematics | Immersion (mathematics) | Inclusion map | Embedding | Link (knot theory) | Sheaf (mathematics) | Configuration space (mathematics) | Taylor series | Homogeneous polynomial | Algebraic topology