In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output...

In the theory of operads in algebra and algebraic topology, an A∞-operad is a parameter space for a multiplication map that is homotopy coherently associative...

algebra, an operad algebra is an "algebra" over an operad. It is a generalization of an associative algebra over a commutative ring R, with an operad replacing...

In the theory of operads in algebra and algebraic topology, an E∞-operad is a parameter space for a multiplication map that is associative and commutative...

In mathematics, the Lie operad is an operad whose algebras are Lie algebras. The notion (at least one version) was introduced by Ginzburg & Kapranov (1994)...

More abstractly, in the language of operad theory, one can consider vector spaces to be algebras over the operad R ∞ {\displaystyle \mathbf {R} ^{\infty...

In algebra, a higher-order operad is a higher-dimensional generalization of an operad. Opetope Heuts, Gijs; Hinich, Vladimir; Moerdijk, Ieke (2016). "On...

introduced the notion of a quadratic operad and defined the quadratic dual of such an operad. Very roughly, an operad is an algebraic structure consisting...

algebra over the little interval operad. This is an example of an A ∞ {\displaystyle A_{\infty }} -operad, i.e. an operad of topological spaces which is...

In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally...

finite products). A more recent development in category theory is operad theory – an operad is a set of operations, similar to a universal algebra, but restricted...

in particular, for the May spectral sequence and for coining the term operad. May received a Bachelor of Arts degree from Swarthmore College in 1960...

several variables. Multicategories are also sometimes called operads, or colored operads. A (non-symmetric) multicategory consists of a collection (often...

(see Mumford measure), semi-infinite cohomology, operads in quantum field theory (see Swiss-cheese operad), Deligne's and Kontsevich's conjectures on Hochschild...

planar operad is the set of all the planar tangles (up to isomorphism) with such compositions. A planar algebra is a representation of the planar operad; more...

a structure that behaves like an algebra over a field. Algebra over an operad Alternative algebra Clifford algebra Composition algebra Differential algebra...

Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and the Deligne conjecture". Conférence Moshé Flato 1999, Vol. I (Dijon)...

of San Diego Williams College Thesis Tesselations of moduli spaces and the mosaic operad (1999) Doctoral advisor Jack Morava Website satyandevadoss.org...

Moerdijk & Weiss (2007). They have the same relation to (colored symmetric) operads, also called symmetric multicategories, that simplicial sets have to categories...

to: E-infinity ring, a commutative ring construct in homotopy theory E∞-operad, a set of contractible maps that are commutative and associative E-infinity...

Lie algebra representation Lie bialgebra Lie coalgebra Lie n-algebra Lie operad Particle physics and representation theory Lie superalgebra Orthogonal symmetric...

a homotopy algebra using the theory of operads: that is, a homotopy Lie algebra is an algebra over an operad in the category of chain complexes over...

Press. ISBN 978-0-521-89485-2. Leinster, Tom [in German] (2004). Higher Operads, Higher Categories. London Math. Society Lecture Note Series. Vol. 298...

Foundation. Holtkamp, Ralf (2006), "On Hopf algebra structures over free operads", Advances in Mathematics, 207 (2): 544–565, arXiv:math/0407074, doi:10...

data analysis, and social choice theory. "Formality of the little N-discs operad", with P. Lambrechts, Memoirs of the American Mathematical Society, 239...

Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and Deligne's conjecture". Conférence Moshé Flato 1999: Quantization, Deformations...

presheaf on the category of opetopes. higher-order operad Leinster, Tom (2004). "Opetopes". Higher Operads, Higher Categories. London Mathematical Society...

ISBN 978-0-393-97141-5. "Strauss Created New Orchestra in Writing His Operad Ariadne". Montreal Gazette. November 26, 1946. Rebecca Paller (October 12...

Sistemy, 9: 30–43, MR 0209178. Weber, Mark (2013), "Free products of higher operad algebras", TAC, 28 (2): 24–65. Weisstein, Eric W. "Graph Cartesian Product"...

and musical composition. Hypergraph Modeling language Ontology language Operad theory Orgology Universal algebra Universal logic Spivak, David I.; Kent...