Results 11 to 20 of about 6,340 (111)
Enriched $\infty$-operads [PDF]
Advances in Mathematics, 2017 Accepted version, 59 ...
Chu, Hongyi, Haugseng, Rune
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Categorified Cyclic Operads [PDF]
Applied Categorical Structures, 2019 In this paper, we introduce a notion of categorified cyclic operad for set-based cyclic operads with symmetries. Our categorification is obtained by relaxing defining axioms of cyclic operads to isomorphisms and by formulating coherence conditions for these isomorphisms.
Pierre-Louis Curien, Jovana Obradović
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From homotopy operads to infinity-operads [PDF]
Journal of Noncommutative Geometry, 2017 The goal of the present paper is to compare, in a precise way, two approaches of operads up to homotopy which appear in the literature. Namely, we construct a functor from the category of strict unital homotopy colored operads to the category of infinity-operads. The former notion, that we make precise, is the operadic generalization of the notion of A-
Grignou, Brice Le
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Communications in Mathematics, 2022 An algebra with identities (a, b, c) = (a, c, b) = (b, a, c) is called assosymmetric, where (x, y, z) = x(yz) − (xy)z is associator. We establish that operad of assosymmetric algebras is not Koszul. We study Sn-module, An-module and GLn-module structures on multilinear parts of assosymmetric operad.
Zhakhayev, Bekzat +2 more
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Simplicial Operads and ∞-Operads
, 2022 AbstractIn this final chapter we fulfil one of the main promises of this book, namely we prove that the homotopy theory of ∞-operads is equivalent to that of simplicial (or topological) operads. To prepare for this, Sections 14.1 and 14.2 establish some rather classical material on the homotopy theory of simplicial categories, most of it going back to ...
Gijs Heuts, Ieke Moerdijk
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Formal Lagrangian Operad [PDF]
International Journal of Mathematics and Mathematical Sciences, 2010 Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of the Lagrangian submanifolds of via symplectic reduction. If M is also a symplectic groupoid, then its multiplication space is an associative product in this operad.
Cattaneo Alberto S. +2 more
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Manin products, Koszul duality, Loday algebras and Deligne conjecture [PDF]
, 2006 In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads ...
Balavoine D. +23 more
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Algebraic theories of power operations
Journal of Topology, Volume 16, Issue 4, Page 1543-1640, December 2023., 2023 Abstract We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well‐behaved theories of power operations for E∞$\mathbb {E}_\infty$ ring spectra.
William Balderrama
wiley +1 more source
Lax monoidal adjunctions, two‐variable fibrations and the calculus of mates
Proceedings of the London Mathematical Society, Volume 127, Issue 4, Page 889-957, October 2023., 2023 Abstract We provide a calculus of mates for functors to the ∞$\infty$‐category of ∞$\infty$‐categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformations correspond to maps of (co)cartesian fibrations that do not necessarily preserve (co)cartesian edges. As a sample application, we obtain an equivalence between
Rune Haugseng +3 more
wiley +1 more source