[图书][B] Higher categories and homotopical algebra

DC Cisinski - 2019 - books.google.com
This book provides an introduction to modern homotopy theory through the lens of higher
categories after Joyal and Lurie, giving access to methods used at the forefront of research …

[HTML][HTML] Enriched∞-categories via non-symmetric∞-operads

D Gepner, R Haugseng - Advances in mathematics, 2015 - Elsevier
We set up a general theory of weak or homotopy-coherent enrichment in an arbitrary
monoidal∞-category. Our theory of enriched∞-categories has many desirable properties; …

Q-system completion for C⁎ 2-categories

Q Chen, RH Palomares, C Jones, D Penneys - Journal of Functional …, 2022 - Elsevier
A Q-system in a C⁎ 2-category is a unitary version of a separable Frobenius algebra object
and can be viewed as a unitary version of a higher idempotent. We define a higher unitary …

Emergent generalized symmetries in ordered phases and applications to quantum disordering

SD Pace - SciPost Physics, 2024 - scipost.org
We explore the rich landscape of higher-form and non-invertible symmetries that emerge at
low energies in generic ordered phases. Using that their charge is carried by homotopy …

Dilations and information flow axioms in categorical probability

T Fritz, T Gonda, NG Houghton-Larsen… - … Structures in Computer …, 2023 - cambridge.org
We study the positivity and causality axioms for Markov categories as properties of dilations
and information flow and also develop variations thereof for arbitrary semicartesian …

Generalized symmetries in singularity-free nonlinear models and their disordered phases

SD Pace, C Zhu, A Beaudry, XG Wen - Physical Review B, 2024 - APS
We study the nonlinear σ-model in (d+ 1)-dimensional space-time with connected target
space K and show that, at energy scales below singular field configurations (such as …

Pregeometric spaces from wolfram model rewriting systems as homotopy types

XD Arsiwalla, J Gorard - International Journal of Theoretical Physics, 2024 - Springer
How do spaces in physics emerge from pregeometric discrete building blocks governed by
computational rules? To address this question we investigate non-deterministic rewriting …

Homotopies in Multiway (Non-Deterministic) Rewriting Systems as -Fold Categories

XD Arsiwalla, J Gorard, H Elshatlawy - arXiv preprint arXiv:2105.10822, 2021 - arxiv.org
We investigate algebraic and compositional properties of abstract multiway rewriting
systems, which are archetypical structures underlying the formalism of the Wolfram model …

How to count structure

TW Barrett - Noûs, 2022 - Wiley Online Library
There is sometimes a sense in which one theory posits 'less structure'than another.
Philosophers of science have recently appealed to this idea both in the debate about …

[图书][B] Structure and equivalence

N Dewar - 2022 - cambridge.org
This Element explores what it means for two theories in physics to be equivalent (or
inequivalent), and what lessons can be drawn about their structure as a result. It does so …