Foundations of mathematics | Sheaf theory | Topos theory
In mathematics, a topos (UK: /ˈtɒpɒs/, US: /ˈtoʊpoʊs, ˈtoʊpɒs/; plural topoi /ˈtoʊpɔɪ/ or /ˈtɒpɔɪ/, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion of localization; they are a direct generalization of point-set topology. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic. The mathematical field that studies topoi is called topos theory. (Wikipedia).
5 Best Practices In DevOps Culture | What is DevOps? | Edureka
🔥𝐄𝐝𝐮𝐫𝐞𝐤𝐚 𝐃𝐞𝐯𝐎𝐩𝐬 𝐏𝐨𝐬𝐭 𝐆𝐫𝐚𝐝𝐮𝐚𝐭𝐞 𝐏𝐫𝐨𝐠𝐫𝐚𝐦 𝐰𝐢𝐭𝐡 𝐏𝐮𝐫𝐝𝐮𝐞 𝐔𝐧𝐢𝐯𝐞𝐫𝐬𝐢𝐭𝐲: https://www.edureka.co/executive-programs/purdue-devops This tutorial explains what is DevOps. It will help you understand some of its best practices in DevOps culture. This video will also provide an insight into how different
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DevOps is a word used a lot these days and reading job ads it seems like it's something one person in a team does. It also looks as if I buy the right tools I'm doing DevOps, but is that it? Björn is a programmer with lots of strong opinions, weakly held. When he's not busy changing his mi
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Karl Popper on Definitions (1974)
A version of an upload from the previous channel. It comes from a 1974 interview with Popper. The translation is my own. For more Popper: https://www.youtube.com/playlist?list=PLhP9EhPApKE_VarWCx1d_Uogn_GxsVf-o More Short Clips: https://www.youtube.com/playlist?list=PLhP9EhPApKE8v8UVlc7Ju
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Jens Hemelaer - Toposes of presheaves on monoids as generalized topological spaces
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/HemelaerSlidesToposesOnline.pdf Various ideas from topology have been generalized to toposes, for example surjection
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Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
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
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Nonetheless one should learn the language of topos: Grothendieck... - Colin McLarty [2018]
Grothendieck's 1973 topos lectures Colin McLarty 3 mai 2018 In the summer of 1973 Grothendieck lectured on several subjects in Buffalo NY, and these lectures were recorded, including 33 hours on topos theory. The topos lectures were by far the most informal of the series, with the most si
From playlist Number Theory
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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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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Emily Riehl: On the ∞-topos semantics of homotopy type theory: All ∞-toposes have... - Lecture 3
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 24, 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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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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Morgan Rogers - Toposes of Topological Monoid Actions
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/RogersSlidesToposesOnline.pdf We explain the properties of the familiar properties of continuous actions of groups o
From playlist Toposes online