Concept

Weak equivalence (homotopy theory)

Publications associées (21)

Reduced representations of complexes, signals, and multifiltrations

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Quasi-categories vs. Segal spaces: Cartesian edition

Nima Rasekh

We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: 1.On marked simplicial sets (due to Lurie [31]), 2.On bisimplicial spaces (due to deBrito [12]), 3.On bisimplicial sets, 4.On m ...

2021

On Topological Equivalence in Linear Quadratic Optimal Control

Daniel Kuhn, Wouter Jongeneel

Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...

2021

Filter quotients and non-presentable (∞,1)-toposes

Nima Rasekh

We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -ca ...

2021

Serre-Tate theory for Calabi-Yau varieties

Maciej Emilian Zdanowicz

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

WALTER DE GRUYTER GMBH2021

The Homotopy Theory Of Coalgebras Over Simplicial Comonads

Kathryn Hess Bellwald, Magdalena Kedziorek

We apply the Acyclicity Theorem of Hess, Kedziorek, Riehl, and Shipley (recently corrected by Garner, Kedziorek, and Riehl) to establishing the existence of model category structure on categories of coalgebras over comonads arising from simplicial adjuncti ...

INT PRESS BOSTON, INC2019

Rational SO(2)- equivariant spectra

Magdalena Kedziorek

We prove that the category of rational SO(2)-equivariant spectra has a simple algebraic model. Furthermore, all of our model categories and Quillen equivalences are monoidal, so we can use this classification to understand ring spectra and module spectra v ...

Geometry & Topology Publications2017

A necessary and sufficient condition for induced model structures

Kathryn Hess Bellwald, Magdalena Kedziorek

A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically much harder is to lift the cofibrations and weak equivalence ...

Wiley2017

A Looping-Delooping Adjunction For Topological Spaces

Martina Rovelli

Every principal G-bundle over X is classified up to equivalence by a homotopy class X -> BG, where BG is the classifying space of G. On the other hand, for every nice topological space X Milnor constructed a strict model of its loop space (Omega) over tild ...

Int Press Boston, Inc2017

Cellular Homotopy Excision

Kay Remo Werndli

There is a classical "duality" between homotopy and homology groups in that homotopy groups are compatible with homotopy pullbacks (every homotopy pullback gives rise to a long exact sequence in homotopy), while homology groups are compatible with homotopy ...

EPFL2016