Homotopy theory | Objects (category theory)

Fibrant object

In mathematics, specifically in homotopy theory in the context of a model category M, a fibrant object A of M is an object that has a fibration to the terminal object of the category. (Wikipedia).

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Stable Homotopy Seminar, 9: Infinite Loop Spaces, and Homotopy Colimits

The fibrant spectra are the Ω-spectra, and we can give an elegant explicit description of the fibrant replacement. The "infinite loop space" functor, which is the derived right adjoint to the suspension spectrum, is then given by taking the 0th space of an equivalent Ω-spectrum. This allow

From playlist Stable Homotopy Seminar

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Benno van den Berg: Univalent polymorphism

The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category EFF. Path categories are categories of fibrant objects in the se

From playlist Workshop: "Types, Homotopy, Type theory, and Verification"

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Alexander Neshitov - Fibrant Resolutions of Motivic Thom Spectra

Notes: https://nextcloud.ihes.fr/index.php/s/gwxKFPnX5xTzmXS This is a joint work with G. Garkusha. In the talk I will discuss the construction of fibrant replacements for spectra consisting of Thom spaces (suspension spectra of varieties and algebraic cobordism 𝑀𝐺𝐿 being the motivating e

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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What are collinear points

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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Daniel Bennequin - Topos, stacks, semantic information and artificial neural networks

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Joint work with Jean-Claude Belfiore Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck’s topos; its learning dynamic correspo

From playlist Toposes online

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Anders Mörtberg: Yet Another Cartesian Cubical Type Theory yacctt

The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: I will discuss recent work on developing a Cartesian cubical type theory inspired by the computational semantics of Computational Higher Type Theory of Angiuli et. al. Th

From playlist Workshop: "Types, Homotopy, Type theory, and Verification"

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Wojciech Chachólski (4/29/20): TDA invariants and model categories

Title: TDA invariants and model categories Abstract: Data analysis is a balancing act of simplification and ignoring most of the information available on the one hand, and retaining what might be meaningful for the particular task on the other. The same balancing act of extracting simplif

From playlist AATRN 2020

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Viktoriya Ozornova: Equivalences in higher categories

CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR

From playlist Topology

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What are opposite rays

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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What are opposite rays

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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What are opposite Rays

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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Dimensions (1 of 3: The Traditional Definition - Directions)

More resources available at www.misterwootube.com

From playlist Exploring Mathematics: Fractals

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What is the definition of a ray

👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

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Special Relativity F2 Relativistic Addition of Velocities

The relativistic addition of velocities.

From playlist Physics - Special Relativity

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Paul Bendich (5/12/21): Data Complexes, Obstructions, Persistent Data Merging

Title: Data Complexes, Obstructions, Persistent Data Merging Abstract: Data complexes provide a mathematical foundation for semi-automated data-alignment tools that are common in commercial database software. We develop theory that shows that database JOIN operations are subject to genuin

From playlist AATRN 2021

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What is a Symmetry?

Symmetries show up everywhere in physics. But what is a symmetry? While the symmetries of shapes can be interesting, a lot of times, we are more interested in symmetries of space or symmetries of spacetime. To describe these, we need to build "invariants" which give a mathematical represen

From playlist Relativity

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A Relative Calabi-Yau Structure for Legendrian Contact Homology - Georgios Dimitroglou Rizell

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar 9:15am|Remote Access Topic: A Relative Calabi-Yau Structure for Legendrian Contact Homology Speaker: Georgios Dimitroglou Rizell Affiliation: Uppsala University Date: March 31, 2023 The duality long exact sequence re

From playlist Mathematics

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Jean-Louis Colliot-Thélène : H3 non ramifié et cycles de codimension 2

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebraic and Complex Geometry

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Special Relativity B4 Time Dilation

Relativistic time dilation.

From playlist Physics - Special Relativity

Related pages

Fibration | Mathematics | Kan fibration | Homotopy group | Homotopy theory | Cofibration | Simplicial set | Category (mathematics) | Model category