Functors | Homotopy theory | Simplicial sets
In mathematics, more specifically in homotopy theory, a simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets). Equivalently, a simplicial presheaf is a simplicial object in the category of presheaves on a site. The notion was introduced by A. Joyal in the 1970s. Similarly, a simplicial sheaf on a site is a simplicial object in the category of sheaves on the site. Example: Consider the étale site of a scheme S. Each U in the site represents the presheaf . Thus, a simplicial scheme, a simplicial object in the site, represents a simplicial presheaf (in fact, often a simplicial sheaf). Example: Let G be a presheaf of groupoids. Then taking nerves section-wise, one obtains a simplicial presheaf . For example, one might set . These types of examples appear in K-theory. If is a local weak equivalence of simplicial presheaves, then the induced map is also a local weak equivalence. (Wikipedia).
Prealgebra Lecture 3.1 Part 1: Simplifying Algebraic Expressions
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Prealgebra Lecture 3.1 Part 3: Simplifying Algebraic Expressions
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Georg Biedermann - Higher Sheaves
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Joint work with Mathieu Anel, Eric Finster, and André Joyal Even though on the surface the theories look similar, there are basic differences between the classical theory of 1-t
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Prealgebra Lecture 3.1 Part 2: Simplifying Algebraic Expressions
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Prealgebra Lecture 3.1 Part 8: Simplifying Algebraic Expressions
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Prealgebra Lecture 3.1 Part 9: Simplifying Algebraic Expressions
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Dustin Clausen - Toposes generated by compact projectives, and the example of condensed sets
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos. The next simplest topology ha
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Prealgebra Lecture 3.1 Part 4: Simplifying Algebraic Expressions
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Prealgebra Lecture 2.2 Part 2: Adding Integers
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Anna Carla RUSSO - Morita-equivalences for MV-algebras
We shall make a survey of the most recent results obtained in connection with the programme of investigating notable categorical equivalences for MV-algebras from a topos-theoretic perspective commenced in [3]. In [3] and [2] we generalize to a topos-theoretic setting two classical equival
From playlist Topos à l'IHES
Prealgebra Lecture 2.2 Part 1: Adding Integers
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Riccardo Zanfa - Extending the topological presheaf-bundle adjunction to sites and toposes
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/ZanfaSlidesToposesOnline.pdf Riccardo Zanfa: “Extending the topological presheaf-bundle adjunction to sites and topo
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Olivia Caramello - 3/4 ntroduction to categorical logic, classifying toposes...
Introduction to categorical logic, classifying toposes and the 'bridge' technique Theories classified by a presheaf topos and their quotients. Finite presentability, irreducible formulae and homogeneous models.
From playlist Topos à l'IHES
Mr LIMA de CARVALHO e SILVA - From Essential Inclusions to Local Geometric Morphisms
It is well known that, given a site of denition, a subtopos of Grothendieck topos can be obtained by strengthening the Grothendieck topology, thus obtaining an inclusion of toposes. An essential inclusion is one where the inverse image functor of this inclusion has a left adjoint. Kelly an
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Paul André Melliès: Refinement type systems and Martin Lof type theory
Please Note: Due to technical issues the recordings of the blackboard are shown in a slideshow manner. The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In this talk, I will review my recent work with Noam Zeilberger on
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
Prealgebra Lecture 4.2 Part 2: Prime Factorization and Simplification of Fractions
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Emily Riehl: On the ∞-topos semantics of homotopy type theory: The simplicial model of...- Lecture 2
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 22, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
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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)
Prealgebra Lecture 3.1 Part 5: Simplifying Algebraic Expressions
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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