Concept
Higher category theory
Related publications (50)
Seeding and Emergence of Composite Skyrmions in a van der Waals Magnet
Klaus Kern, Marko Burghard, Lukas Powalla
Topological charge plays a significant role in a range of physical systems. In particular, observations of real-space topological objects in magnetic materials have been largely limited to skyrmions - states with a unitary topological charge. Recently, mor ...
WILEY-V C H VERLAG GMBH2023Hopf algebras and Hopf-Galois extensions in infinity-categories
In this thesis, we study interactions between algebraic and coalgebraic structures in infinity-categories (more precisely, in the quasicategorical model of (infinity, 1)-categories). We define a notion of a Hopf algebra H in an E-2-monoidal infinity-catego ...
EPFL2022Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes
Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...
NATURE PORTFOLIO2022A Shadow Perspective on Equivariant Hochschild Homologies
Kathryn Hess Bellwald, Inbar Klang
Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...
OXFORD UNIV PRESS2022The Economics of Incomplete Plan - on Conditions, Procedures and Design of Future Mission - Oriented Innovation Policies
The buzzword in industrial policy and innovation policy circles is mission-oriented innovation policy (MOIP) -which means a policy to encourage innovation intended to accomplish a certain missionwhether it be a societal challenge (climate change, global he ...
INST ESTUDIOS FISCALES2022On minimal tilting complexes in highest weight categories
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie ...
2022Homotopical relations between 2-dimensional categories and their infinity-analogues
In this thesis, we study the homotopical relations of 2-categories, double categories, and their infinity-analogues. For this, we construct homotopy theories for the objects of interest, and show that there are homotopically full embeddings of 2-categories ...
EPFL2021Quasi-categories vs. Segal spaces: Cartesian edition
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 ...
2021The cotangent complex and Thom spectra
The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of E-infinity-ring spectra in various ways. In this work we first establish, in the context o ...
2021Filter quotients and non-presentable (∞,1)-toposes
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