We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
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
algebraic geometry 25 Morphisms of varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of a morphism of varieties and compares algebraic varieties with other types of locally ringed spaces.
From playlist Algebraic geometry I: Varieties
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Weil conjectures 7: What is an etale morphism?
This talk explains what etale morphisms are in algebraic geometry. We first review etale morphisms in the usual topology of complex manifolds, where they are just local homeomorphism, and explain why this does not work in algebraic geometry. We give a provisional definition of etale morphi
From playlist Algebraic geometry: extra topics
Category Theory 2.2: Monomorphisms, simple types
Monomorphisms, simple types.
From playlist Category Theory
Category theory for JavaScript programmers #19: some formality around categories
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Higher algebra 4: Derived categories as ∞-categories
In this video, we construct the ∞-categorical refinement of the derived category of an abelian category. This is the fourth video in our introduction to ∞-categories and Higher Algebra. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA
From playlist Higher Algebra
Higher Algebra 1: ∞-Categories
In this video, we introduce ∞-categories. This is the first of a series of videos towards a reasonably non-technical overview over stable ∞-categories and Higher Algebra, which are intended to be watchable independently from the main lecture. Further resources: M.Boardman and R.Vogt. Homo
From playlist Higher Algebra
Shadows of Computation - Lecture 2 - When are two mathematical objects the same?
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 second lecture Billy
From playlist Shadows of Computation
Generic bases for cluster algebras (Lecture 2) by Pierre-Guy Plamondon
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
Landau-Ginzburg - Seminar 1 - Introduction
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this first lecture Dan Murfet gives a high level overview of the seminar, singularities and the 1-morphisms of LG. The main example is how to think about permu
From playlist Metauni
Commutative algebra 46: Limits and colimits of modules
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We define limits and colimits of modules, and give several examples (direct sums and products, kernels, cokernels, inverse lim
From playlist Commutative algebra
Cluster characters, generic bases for cluster algebras (Lecture 4) by Pierre-Guy Plamondon
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
Homotopy Category As a Localization by Rekha Santhanam
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Lecture 7: Sheaves of sets (Part 2)
The most important examples of topoi are categories of sheaves of sets on a small category. Patrick Eilliott introduced this class of examples over two talks, of which is the second. In this talk he defines Grothendieck topologies and the category of sheaves on a site, and develops the exa
From playlist Topos theory seminar
Here we describe what morphisms of derived categories look like using some properties of injective resolutions we don't prove.
From playlist Derived Categories