Category theory

Lifting property

In mathematics, in particular in category theory, the lifting property is a property of a pair of morphisms in a category. It is used in homotopy theory within algebraic topology to define properties of morphisms starting from an explicitly given class of morphisms. It appears in a prominent way in the theory of model categories, an axiomatic framework for homotopy theory introduced by Daniel Quillen. It is also used in the definition of a factorization system, and of a weak factorization system, notions related to but less restrictive than the notion of a model category. Several elementary notions may also be expressed using the lifting property starting from a list of (counter)examples. (Wikipedia).

Lifting property
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Lecture 3D - Lifting with a Pulley

Here is what pulleys are good for. They can apply the tension force multiple times for a "mechanical advantage". In this problem we go through the tensions and weights, and think about the effect on motion.

From playlist PHYS 125 | Forces

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Cable drive 19

W: weight of the load P: pulling force for moving up the load. Mechanical advantage: 4

From playlist Mechanisms

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Cable drive 17b

W: weight of the load P: pulling force for moving up the load. Mechanical advantage: 8

From playlist Mechanisms

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Physical Science 2.6b - Gravity

Weight, the force due to gravity, and the acceleration caused by this force.

From playlist Physical Science Chapter 2 (Complete chapter)

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How To Lift THE WORLD!!!

How To Lift ANYTHING With A Simple Lever!! #Physics #Mechanical #Engineering #Math #NicholasGKK #Shorts

From playlist General Mechanics

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Physical Science 3.3d - Hydraulic Lift

An example problem. Calculating the lifting force from a hydraulic lift given the force and the areas involved. The problem is worked out and explained.

From playlist Physical Science Chapter 3 (Complete chapter)

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The Difference Between Mass and Weight

There is a common perception that weight and mass are basically the same thing. This video aims to tease out the difference between mass and weight by asking people what makes a car difficult to push. The standard answer is that it is difficult to push because it's heavy. But heaviness is

From playlist Inertia

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Physical Science 3.3c - Hydraulic Lift

The means by which a hydraulic lift creates a large force is explained in light of Pascal's Law and the transmission of pressure through a fluid.

From playlist Physical Science Chapter 3 (Complete chapter)

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Why Is SLIDING Easier?!?

Why Is It Easier To SLIDE An Object, Rather Than LIFT It?!? #Physics #Mechanics #Friction #Study #NicholasGKK #Shorts

From playlist General Mechanics

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Gilles Pisier: The lifting property for C*-algebras

Talk by Gilles Pisier in Global Noncommutative Geometry Seminar (Americas) on January 14, 2022 in https://globalncgseminar.org/talks/the-lifting-property-for-c-algebras/

From playlist Global Noncommutative Geometry Seminar (Americas)

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Gilles Pisier - Propriétés de relèvement pour les 𝐶^∗-algèbres : du local au global ?

The main problem we will consider is whether the local lifting property (LLP) of a $C^*$-algebra implies the (global) lifting property (LP). Kirchberg showed that this holds if the Connes embedding problem has a positive solution, but it might hold even if its solution is negative. We will

From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”

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Stable Homotopy Seminar, 7: Constructing Model Categories

A stroll through the recognition theorem for cofibrantly generated model categories, using it to construct (1) the Quillen/Serre model structure on topological spaces and (2) the levelwise model structure on spectra. The latter captures the idea that spectra are sequences of spaces, but no

From playlist Stable Homotopy Seminar

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Introduction to Homotopy Theory: Part 6- Projective and Injective Morphisms

Credits: nLab: https://ncatlab.org/nlab/show/Introdu...​ Animation library: https://github.com/3b1b/manim​​​​ My own code/modified library: https://github.com/treemcgee42/youtube Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track L

From playlist Introduction to Homotopy Theory

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Stable Homotopy Seminar, 5: The Small Object Argument (Samuel Mercier)

Samuel Mercier discusses cofibrant generation of model categories and the small object argument, a vital tool allowing us to construct model categories with functorial factorization. As an application, he defines the levelwise model structure on spectra. ~~~~~~~~~~~~~~~~==================

From playlist Stable Homotopy Seminar

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Stable Homotopy Seminar, 4: Model categories (Ivo Vekemans)

This talk by Ivo Vekemans is a thorough introduction to model categories, presenting: weak factorization systems; the definition of model category and major examples (simplicial sets, topological spaces, and chain complexes); notions of homotopy in a model category, and the homotopy catego

From playlist Stable Homotopy Seminar

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Lifting small locally testable codes (LTCs) to large LTCs via HDXs - Prahladh Harsha

Computer Science/Discrete Mathematics Seminar I Topic: Lifting small locally testable codes (LTCs) to large LTCs via HDXs Speaker: Prahladh Harsha Affiliation: Tata Institute of Fundamental Research Date: November 25, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

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Introduction to Homotopy Theory- Part 4: Fibrations

Wow! This one was a lot more detailed than usual, so I'd really recommend going through the proofs with the nLab in hand. I tried to elucidate some of their explanations, but it's still good to have both, so hopefully in between both of our presentations you can find understanding. And as

From playlist Introduction to Homotopy Theory

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Galois Representations 4 by Shaunak Deo

PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA

From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)

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Simple Machines (1 of 7) Pulleys; Defining Forces, Distances and MA

For the pulley simple machine this video defines the terms input and output force, input and output distance and mechanical advantage. A simple machine is a mechanical device that changes the direction and the magnitude of a force. In general, they can be defined as the simplest mechanis

From playlist Mechanics

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Order (group theory) | Topological space | Injective module | Metric space | Torsion (algebra) | Pure subgroup | Continuous function | Free group | T1 space | Group (mathematics) | Algebraic topology | Isomorphism | Weak factorization system | Pullback (category theory) | Chain complex | Homotopy theory | Product (category theory) | Simplicial set | Hausdorff space | Finite group | Disjoint union | Factorization system | Projective module | Complete metric space | Dense set | Pushout (category theory) | Connected space | Mathematics | Set (mathematics) | P-group | Homotopy lifting property | Embedding | Cyclic group | Category theory | Category (mathematics) | Subset | Trivial topology | Subgroup | Kolmogorov space | Normal space | Discrete space | Image (mathematics) | Module (mathematics) | Commutative ring