Category theory | Homological algebra

In mathematics, Alexander Grothendieck in his "Tôhoku paper" introduced a sequence of axioms of various kinds of categories enriched over the symmetric monoidal category of abelian groups. Abelian categories are sometimes called AB2 categories, according to the axiom (AB2). AB3 categories are abelian categories possessing arbitrary coproducts (hence, by the existence of quotients in abelian categories, also all colimits). AB5 categories are the AB3 categories in which filtered colimits of exact sequences are exact. Grothendieck categories are the AB5 categories with a generator. (Wikipedia).

👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

Étale cohomology lecture 3, August 27, 2020

Sites and sheaves, the étale and fppf site, representable functors

From playlist Étale cohomology and the Weil conjectures

Étale cohomology lecture 5 - 9/3/2020

Fppf descent part 2, intro to the category of sheaves

From playlist Étale cohomology and the Weil conjectures

Poop kind of stinks, but the stuff inside of poop can tell us a lot about the natural world. Hosted by: Hank Green SciShow has a spinoff podcast! It's called SciShow Tangents. Check it out at http://www.scishowtangents.org ---------- Support SciShow by becoming a patron on Patreon: https

From playlist Biology

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

👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

Introduction to the C programming language. Part of a larger series teaching programming. See http://codeschool.org

From playlist The C language

Introduction to the C programming language. Part of a larger series teaching programming. See http://codeschool.org

From playlist The C language

All F chords are made from different permutations and combinations of the F,C and A notes

From playlist Music Lessons

What is an equilateral triangle

👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

From playlist Types of Triangles and Their Properties

On the classification of fusion categories – Sonia Natale – ICM2018

Algebra Invited Lecture 2.5 On the classification of fusion categories Sonia Natale Abstract: We report, from an algebraic point of view, on some methods and results on the classification problem of fusion categories over an algebraically closed field of characteristic zero. © Interna

From playlist Algebra

Charles Rezk - 1/4 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/RezkNotesToposesOnlinePart1.pdf In this series of lectures I will give an introduction to the concept of "infinity

From playlist Toposes online

The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories - Emily Riehl

Vladimir Voevodsky Memorial Conference Topic: The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories Speaker: Emily Riehl Affiliation: Johns Hopkins University Date: September 12, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Stable Homotopy Seminar, 14: The stable infinity-category of spectra

I give a brief introduction to infinity-categories, including their models as simplicially enriched categories and as quasi-categories, and some categorical constructions that also make sense for infinity-categories. I then describe what it means for an infinity-category to be stable and h

From playlist Stable Homotopy Seminar

Category Theory 3.1: Examples of categories, orders, monoids

Examples of categories, orders, monoids.

From playlist Category Theory

Homotopy Category As a Localization by Rekha Santhanam

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From playlist Dualities in Topology and Algebra (Online)

From playlist Types of Triangles and Their Properties