Lecture 12: Classifying topoi (Part 1)
This is the first of several talks on the subject of classifying topoi. I began with a brief reminder of the overall picture from the first talk, i.e. what are classifying topoi and why do we care (from the point of view of organising mathematics). Then I spent some time talking about tens
From playlist Topos theory seminar
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
Olivia Caramello - 2/4 ntroduction to categorical logic, classifying toposes...
Introduction to categorical logic, classifying toposes and the « bridge » technique Construction of classifying toposes for geometric theories. Duality between the subtoposes of the classifying topos of a geometric theory and the quotients of the theory. Transfer of topos‐the
From playlist Topos à l'IHES
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
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
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
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
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
Joshua Wrigley - The Logic and Geometry of Localic Morphisms
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/WrigleySlidesToposesOnline.pdf In this presentation, a substitutive syntactic site for the classifying topos of a ge
From playlist Toposes online
Ming Ng - Adelic Geometry via Topos Theory
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/NgSlidesToposesOnline.pdf Joint work with Steve Vickers In this talk, I will give a leisurely introduction to the t
From playlist Toposes online
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
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
Towards elementary infinity-toposes - Michael Shulman
Vladimir Voevodsky Memorial Conference Topic: Towards elementary infinity-toposes Speaker: Michael Shulman Affiliation: University of San Diego Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
This is video number 4 in the series defining topoi. Here's the updated text used in the video: https://gist.github.com/Nikolaj-K/469b9ca1c085ea4ac4e3d7d0008913f5 Last video: https://youtu.be/Bdn64edr4Ng
From playlist Logic
With Olivia Caramello, André Joyal, Laurent Lafforgue et Alain Connes
From playlist Topos à l'IHES
Matthias Hutzler - Gluing classifying toposes
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/
From playlist Toposes online
Lecture 4: The definition of a topos (Part 1)
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 first) James Clift will explain all of these terms in detail. In this talk he defines products, pullbacks, general limits, and exponentials and in Part 2
From playlist Topos theory seminar