Results 1 to 10 of about 92 (88)
$omega$-Operads of coendomorphisms and fractal $omega$-operads for higher structures [PDF]
Categories and General Algebraic Structures with Applications, 2015 In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads.
Camell Kachour
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Operads of higher transformations for globular sets and for higher magmas [PDF]
Categories and General Algebraic Structures with Applications, 2015 In this article we discuss examples of fractal $omega$-operads. Thus we show that there is an $omega$-operadic approach to explain existence of the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French ...
Camell Kachour
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Algebras of Higher Operads as Enriched Categories [PDF]
Applied Categorical Structures, 2008 38pp
Michael Batanin, Mark Weber
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Algebraic & Geometric Topology, 2019 We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category $Ξ$ of trees, which carries a tight relationship to the Moerdijk-Weiss category of rooted trees $Ω$. We prove a nerve theorem exhibiting colored cyclic operads as presheaves on $Ξ$ which satisfy
Hackney, Philip +2 more
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A graphical category for higher modular operads [PDF]
Advances in Mathematics, 2020 We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Quillen model structure on the collection of simplicial presheaves for a certain category of undirected graphs.
Hackney, Philip +2 more
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From operator categories to higher operads [PDF]
Geometry & Topology, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Formality of a higher-codimensional Swiss-cheese operad
Algebraic & Geometric Topology, 2022 47 pages, comments welcome. v3: The operad has been renamed. The abstract, introduction and background sections have been rewritten with a more expert audience in mind and pared down.
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Higher algebra over the Leibniz operad [PDF]
Banach Center Publications, 2017 peer ...
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Box operads and higher Gerstenhaber brackets
, 2023 22 pages + 8 appendix.
Van, Hoang Dinh +2 more
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Higher Operads, Higher Categories [PDF]
, 2004 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.
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