In category theory, a span, roof or correspondence is a generalization of the notion of relation between two objects of a category. When the category has all pullbacks (and satisfies a small number of other conditions), spans can be considered as morphisms in a category of fractions. The notion of a span is due to Nobuo Yoneda (1954) and Jean Bénabou (1967). (Wikipedia).
Category Theory: The Beginner’s Introduction (Lesson 1 Video 4)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed
From playlist Category Theory: The Beginner’s Introduction
Category Theory: The Beginner’s Introduction (Lesson 1 Video 2)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. Follow me on Twitter: @mjmcodr
From playlist Category Theory: The Beginner’s Introduction
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
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
Yonatan Harpaz - New perspectives in hermitian K-theory I
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Winter School JTP: From Hall algebras to legendrian skein algebras, Fabian Haiden
A mysterious relation between Hall algebras of Fukaya categories of surfaces and skein algebras was suggested by recent work of Morton-Samuelson and Samuelson-Cooper. I will discuss how this relation can be made precise using knot theory of legendrian curves and general gluing properties o
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Paul-André Melliès - A gentle introduction to template games and linear logic
Game semantics is the art of interpreting formulas (or types) as games and proofs (or programs) as strategies. In order to reflect the interactive behaviour of pro- grams, strategies are required to follow specific scheduling policies. Typically, in the case of a sequential programming lan
From playlist Combinatorics and Arithmetic for Physics: Special Days 2022
Stable Homotopy Seminar, 1: Introduction and Motivation
We describe some features that the category of spectra is expected to have, and some ideas from topology it's expected to generalize. Along the way, we review the Freudenthal suspension theorem, and the definition of a generalized cohomology theory. ~~~~~~~~~~~~~~~~======================
From playlist Stable Homotopy Seminar
Category Theory: The Beginner’s Introduction (Lesson 1 Video 5)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed
From playlist Category Theory: The Beginner’s Introduction
algebraic geometry 23 Categories
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.
From playlist Algebraic geometry I: Varieties
Newton above Hodge Introduction part 1
We give the definition of Crystals and Spans and explain some of their basic properties.
From playlist Newton above Hodge
Representations of Galois algebras – Vyacheslav Futorny – ICM2018
Lie Theory and Generalizations Invited Lecture 7.3 Representations of Galois algebras Vyacheslav Futorny Abstract: Galois algebras allow an effective study of their representations based on the invariant skew group structure. We will survey their theory including recent results on Gelfan
From playlist Lie Theory and Generalizations
Markus Land - L-Theory of rings via higher categories II
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Mirror symmetry for the mirror quartic, and other stories - Ivan Smith
Workshop on Homological Mirror Symmetry: Methods and Structures Speaker: Ivan Smith Topic: Mirror symmetry for the mirror quartic, and other stories Affiliation: University of Cambridge Date: November, 9, 2016 For more video, visit http://video.ias.edu
From playlist Workshop on Homological Mirror Symmetry: Methods and Structures
Category theory for JavaScript programmers #19: some formality around categories
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
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