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Higher Operads, Higher Categories [PDF]
, 2003 Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. The heart of this book is the language of generalized operads.
Tom Leinster
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Towards higher super-$\sigma$-model categories [PDF]
SciPost Physics Proceedings, 2023 A simplicial framework for the gerbe-theoretic modelling of supercharged-loop dynamics in the presence of worldsheet defects is discussed whose equivariantisation with respect to global supersymmetries of the bulk theory and subsequent orbit ...
Rafał R. Suszek
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Higher quasi-categories vs higher Rezk spaces [PDF]
Journal of K-theory, 2014 We introduce a notion of n-quasi-categories as fibrant objects of a model category structure on presheaves on Joyal's n-cell category \Theta_n. Our definition comes from an idea of Cisinski and Joyal.
Barwick +23 more
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Cartesian closed 2-categories and permutation equivalence in higher-order rewriting [PDF]
Logical Methods in Computer Science, 2013 We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.
Tom Hirschowitz
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Higher Cluster Categories and QFT Dualities [PDF]
Physical Review D, 2017 We present a unified mathematical framework that elegantly describes minimally SUSY gauge theories in even dimension, ranging from $6d$ to $0d$, and their dualities.
Franco, Sebastian, Musiker, Gregg
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Higher homotopy categories, higher derivators, and K-theory [PDF]
Forum of Mathematics, Sigma, 2022 Abstract For every $\infty $ -category $\mathscr {C}$ , there is a homotopy n-category $\mathrm {h}_n \mathscr {C}$ and a canonical functor $\gamma _n \colon \mathscr {C} \to \mathrm {h}_n \mathscr {C}$ .
George Raptis
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Condensations in higher categories [PDF]
, 2019 We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is the closure for absolute limits. Our construction replaces the idempotents in the ordinary version with a notion that we call "condensations." The name is
Davide Gaiotto, Theo Johnson-Freyd
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Higher-dimensional categories with finite derivation type [PDF]
, 2008 We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalizing the one introduced by Squier for ...
Yves Guiraud, Philippe Malbos
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Homomorphisms of higher categories [PDF]
Advances in Mathematics, 2010 We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction is such that these homomorphisms admit a strictly associative and unital composition.
Richard Garner
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Lobe‐Specific Risk of Malignancy in Parotid Gland Lesions: A Milan System‐Based Analysis [PDF]
Laryngoscope Investigative OtolaryngologyPurpose To evaluate the diagnostic accuracy of fine‐needle aspiration cytology (FNAC) for parotid gland lesions using the Milan System while eliminating verification bias, and to systematically compare risk of malignancy (ROM) between superficial and ...
Serkan Şerifler +6 more
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