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
We Need a Bigger Definition of Creativity
► Please Subscribe to My Channel Here - http://bit.ly/spencervideos When you the word “creative,” you might think of a painter or a playwright or an author or a photographer or a filmmaker or a chef. In other words, you might think of people who make things. I think it’s what we mean wh
From playlist What Is Creativity?
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
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
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
Higher Algebra 10: E_n-Algebras
In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin
From playlist Higher Algebra
Duality In Higher Categories II by Pranav Pandit
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)
Duality In Higher Categories IV by Pranav Pandit
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)
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)
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
Derived categories of cyclic covers and their branch divisors - Alexander Perry
Alexander Perry Harvard University April 29, 2015 Given a variety YY with a rectangular Lefschetz decomposition of its derived category, I will discuss an interesting relation between the derived categories of a cyclic cover of YY and its branch divisor. As examples, I will describe the c
From playlist Mathematics
Lucile Vandembroucq (8/25/22): On the weak topological complexity and the TC-Ganea conjecture
By analogy with the classical Ganea conjecture, which has been disproved by N. Iwase, the TC-Ganea conjecture asks whether the equality TC(X x S^n)=TC(X)+TC(S^n) holds for all finite CW complexes X and all positive integers n. In a previous work in collaboration with J. González and M. Gra
From playlist Topological Complexity Seminar
Lecture 6: HKR and the cotangent complex
In this video, we discuss the cotangent complex and give a proof of the HKR theorem (in its affine version) Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-m
From playlist Topological Cyclic Homology
Introduction To Complete Segal Spaces 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)
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
Jamie Scott (9/23/21): Applications of Surgery to a Generalized Rudyak Conjecture
Rudyak’s conjecture states that cat (M) is at least cat (N) given a degree one map f between the closed manifolds M and N. In the recent paper "Surgery Approach to Rudyak's Conjecture", the following theorem was proven: Theorem. Let f from M to N be a normal map of degree one between clos
From playlist Topological Complexity Seminar