[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 …
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; …
monoidal∞-category. Our theory of enriched∞-categories has many desirable properties; …
Q-system completion for C⁎ 2-categories
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 …
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 …
low energies in generic ordered phases. Using that their charge is carried by homotopy …
Dilations and information flow axioms in categorical probability
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 …
and information flow and also develop variations thereof for arbitrary semicartesian …
Generalized symmetries in singularity-free nonlinear models and their disordered phases
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 …
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 …
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 …
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 …
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 …
inequivalent), and what lessons can be drawn about their structure as a result. It does so …