Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 28th 2023
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexA couple of people are working together on relating condensed mathematics to a kind of local cohesiveness. They speak of the concept of a fractured structure/fractured topos, presumably related to [[fracture squares]]. Their talk notes: Qi Zhu, [Fractured structure on condensed spaces](https://1429cecd-24a0-4223-8b7c-1ebf47aa12e2.filesusr.com/ugd/8e912a_8d2a90176ed14969a877e77ec1b787da.pdf); Nima Rasekh, [What is a topological structure?](https://guests.mpim-bonn.mpg.de/rasekh/Condensed.pdf).

   A couple of people are working together on relating condensed mathematics to a kind of local cohesiveness. They speak of the concept of a fractured structure/fractured topos, presumably related to fracture squares.

   Their talk notes: Qi Zhu, Fractured structure on condensed spaces; Nima Rasekh, What is a topological structure?.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 28th 2023
   • (edited Oct 28th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThey are referring to the notion of "fractured $\infty$-topos" in Ch. 20 of *[[Spectral Algebraic Geometry]]* ([pp. 1498](https://math.harvard.edu/~lurie/papers/SAG-rootfile.pdf#page=1498)).

   They are referring to the notion of “fractured $\infty$-topos” in Ch. 20 of Spectral Algebraic Geometry (pp. 1498).