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
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
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
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
Recommended books for the undergrad category theorist
I'll talk more about universal constructions on this channel, so best subscribe. In this video I go through a curated list of introductory text about category theory. You can find the list here: https://gist.github.com/Nikolaj-K/282515e58c1c14de2e25222065f77a0a In the video I comment on a
From playlist Algebra
Ind and Pro Categories Associated to a Category
This is super basic. I ripped this off of ncatlab, one of the best websites on the planet.
From playlist Category Theory
Charles Rezk - 4/4 Higher Topos Theory
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart4.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Jens Hemelaer - Toposes of presheaves on monoids as generalized topological spaces
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/HemelaerSlidesToposesOnline.pdf Various ideas from topology have been generalized to toposes, for example surjection
From playlist Toposes online
Ivan Di Liberti - Towards higher topology
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/DiLibertiSlidesToposesOnline.pdf We categorify the adjunction between locales and topological spaces, this amounts t
From playlist Toposes online
Higher Algebra 11: p-adic completion (corrected)
In this video we introduce the notion of p-adic completion and p-adic equivalence of spectra. We characterize those notions in concrete terms and give examples. Finally we cover the Hasse-square, which can be used to recover X from it completions and its rationalisation. All the material i
From playlist Higher Algebra
Benedikt Ahrens - Univalent Foundations and the UniMath library - IPAM at UCLA
Recorded 13 February 2023. Benedikt Ahrens of Delft University of Technology presents "Univalent Foundations and the UniMath library" at IPAM's Machine Assisted Proofs Workshop. Abstract: Univalent Foundations (UF) were designed by Voevodsky as a foundation of mathematics that is "invarian
From playlist 2023 Machine Assisted Proofs Workshop
Dave Benson: Spectral methods in the representation theory of finite groups - Lecture 3
My intention is to develop the cohomology theory of finite groups and use it to discuss the stable module category and the homotopy category of complexes of injective modules, and to relate them to the modules over cochains on the classifying space. This video is part of a series of lectu
From playlist Summer School: Spectral methods in algebra, geometry, and topology
Bertrand Toën - Deformation quantization and derived algebraic geometry
Bertrand TOËN (CNRS - Univ. de Montpellier 2, France)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
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
Adam Topaz - The Liquid Tensor Experiment - IPAM at UCLA
Recorded 13 February 2023. Adam Topaz of the University of Alberta presents "The Liquid Tensor Experiment" at IPAM's Machine Assisted Proofs Workshop. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/machine-assisted-proofs/
From playlist 2023 Machine Assisted Proofs Workshop