Results 11 to 20 of about 3,791 (108)
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
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Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors
Proceedings of the London Mathematical Society, Volume 127, Issue 3, Page 513-588, September 2023., 2023 Abstract We show that the mesh mutations are the minimal relations among the g${\bm{g}}$‐vectors with respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result to derive geometric properties of the g${\bm{g}}$‐vector fan: we show that the space of all its polytopal realizations is a simplicial cone, and we then ...
Arnau Padrol +3 more
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A 3‐categorical perspective on G$G$‐crossed braided categories
Journal of the London Mathematical Society, Volume 107, Issue 1, Page 333-406, January 2023., 2023 Abstract A braided monoidal category may be considered a 3‐category with one object and one 1‐morphism. In this paper, we show that, more generally, 3‐categories with one object and 1‐morphisms given by elements of a group G$G$ correspond to G$G$‐crossed braided categories, certain mathematical structures which have emerged as important invariants of ...
Corey Jones +2 more
wiley +1 more source
Morita homotopy theory for $(\infty,1)$-categories and $\infty$-operads [PDF]
, 2019 We prove the existence of Morita model structures on the categories of small simplicial categories, simplicial sets, simplicial operads and dendroidal sets, modelling the Morita homotopy theory of $(\infty,1)$-categories and $\infty$-operads.
Caviglia, Giovanni +1 more
core +2 more sources
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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Steps toward the weak higher category of weak higher categories in the globular setting [PDF]
Categories and General Algebraic Structures with Applications, 2016 We start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{Cambat}. As in cite{Cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{N}$, where such weak higher $
Camell Kachour
doaj
Homotopy Batalin-Vilkovisky algebras [PDF]
, 2010 This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties.
Galvez-Carrillo, Imma +2 more
core +10 more sources
Unimodular homotopy algebras and Chern-Simons theory [PDF]
, 2015 Quantum Chern-Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has the structure of an ...
Braun, Christopher, Lazarev, Andrey
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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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