André JOYAL - 3/4 A crash course in topos theory : the big picture
I will sketch an overall picture of topos theory and of the theory of locales. It includes the notion of sheaf on a site, the notion of forcing topology, of geometric morphism and Giraud's theorem. A useful principle is that a topos is a commutative ring-like object. Every topos is a quoti
From playlist Topos à l'IHES
André JOYAL - 4/4 A crash course in topos theory : the big picture
I will sketch an overall picture of topos theory and of the theory of locales. It includes the notion of sheaf on a site, the notion of forcing topology, of geometric morphism and Giraud's theorem. A useful principle is that a topos is a commutative ring-like object. Every topos is a quoti
From playlist Topos à l'IHES
André JOYAL - 2/4 A crash course in topos theory : the big picture
I will sketch an overall picture of topos theory and of the theory of locales. It includes the notion of sheaf on a site, the notion of forcing topology, of geometric morphism and Giraud's theorem. A useful principle is that a topos is a commutative ring-like object. Every topos is a quoti
From playlist Topos à l'IHES
Mathieu ANEL - Toposes are commutative rings
Abstract: In this talk, we shall develop the point of view comparing (higher) toposes to commutative rings. We shall then see how the corresponding integral and differential calculus are related respectively to Verdier duality and Goodwillie calculus of functors.
From playlist Topos à l'IHES
André JOYAL - New variations on the notion of topos
The notion topos is a prominent member of a family of notions which includes that of abelian category, of locally presentable category and of higher topos. We propose two new members: the notion of locus and that of para-topos. The category of pointed spaces and the category of spectra are
From playlist Topos à l'IHES
Charles Rezk - 2/4 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/RezkNotesToposesOnlinePart2.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Topoi 3: The definition of a topos
This is video number 3 in the series defining topoi. Here's the updated text used in the video: https://gist.github.com/Nikolaj-K/469b9ca1c085ea4ac4e3d7d0008913f5 Fourth video on Power and Negation in a topos: https://youtu.be/dvXRQI8RonY
From playlist Algebra
Charles Rezk - 3/4 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/RezkNotesToposesOnlinePart3.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
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)
Lecture 1: Invitation to topos theory
This talk introduces the motivating question for this semester of the Curry-Howard seminar, which is how to organise mathematical knowledge using topoi. The approach sketched out in the talk is via first-order theories, their associated classifying topoi, and adjoint pairs of functors betw
From playlist Topos theory seminar
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
From playlist Toposes online
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
From playlist Toposes online
Jean BÉNABOU - Very, almost, and so on, ...
Very, almost, and so on, ... (when fragments of the language find their way into Topos Theory)
From playlist Topos à l'IHES
Caterina Consani: The Arithmetic Site I
The lecture was held within the framework of the Hausdorff Trimester Program: Non-commutative Geometry and its Applications and the Workshop: Number theory and non-commutative geometry 25.11.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
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
From playlist Toposes online
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
From playlist Toposes online
Antonino Iannazzo, Queen Mary University of London
March 3, Antonino Iannazzo, Queen Mary University of London Differential Algebraic Geometry
From playlist Spring 2023 Online Kolchin Seminar in Differential Algebra
Laurent Lafforgue - 1/4 Classifying toposes of geometric theories
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/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Lecture 5: The definition of a topos (Part 2)
A topos is a Cartesian closed category with all finite limits and a subobject classifier. In his two seminar talks (of which this is the second) James Clift will explain all of these terms in detail. In his first talk he defined products, pullbacks, general limits, and exponentials and in
From playlist Topos theory seminar