Results 21 to 30 of about 120 (113)
The categorical contours of the Chomsky-Sch\"utzenberger representation theorem [PDF]
Logical Methods in Computer ScienceWe develop fibrational perspectives on context-free grammars and on nondeterministic finite-state automata over categories and operads. A generalized CFG is a functor from a free colored operad (aka multicategory) generated by a pointed finite species ...
Paul-André Melliès, Noam Zeilberger
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Journal of Algebra, 2016 We introduce the notion of operadic torsors and operadic quasi-torsors. We show that if an operadic (quasi-)torsor between two operads exists, then these operads are (quasi-)isomorphic. As an application we present the (arguably) shortest known proof of the Deligne conjecture.
Ricardo Campos, Thomas Willwacher
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The Music Box Operad: Random Generation of Musical Phrases from Patterns
Journal of Creative Music SystemsWe introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach to encode musical phrases lies in the fact that it becomes possible to compose multi-patterns in order to produce new ones.
Samuele Giraudo
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Equivariant formality of the little disks operad
Forum of Mathematics, PiThe little n-disks operad is $SO(n)$ and $O(n)$ -equivariantly formal over the rationals. Equivalently, the oriented and unoriented framed little disks operads are rationally formal as $\infty $ -operads.
Pedro Boavida de Brito +2 more
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Operads, Operadic Categories and the Blob Complex
Applied Categorical StructuresAbstractWe will show that the Morrison–Walker blob complex appearing in Topological Quantum Field Theory is an operadic bar resolution of a certain operad composed of fields and local relations. As a by-product we develop the theory of unary operadic categories and study some novel and interesting phenomena arising in this context.
Batanin, M. (Michael) +1 more
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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
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On a Hopf operad containing the Poisson operad [PDF]
Algebraic & Geometric Topology, 2003 A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by generators and relations which have some similarity with the Arnold relations for the cohomology of the type A hyperplane ...
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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 Obradovic
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