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...

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

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...

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...

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)...

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...

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

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

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

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...

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...

geometry; supersymmetry; operads; and Hopf algebras. He retired in 2014. A 2002 book of Markl, Shnider and Stasheff Operads in algebra, topology, and...

{\mathsf {Operads}}\subset {\tfrac {1}{2}}{\mathsf {PROP}}\subset {\mathsf {PROP}}} where the first category is the category of (symmetric) operads. An important...

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

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

sets and bijections between them. Trimble n.d., § 1 Trimble, Todd H. "Notes on the Lie operad" (PDF). University of Chicago. Retrieved 2022-09-27. v t e...

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

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

ISBN 978-0-521-59642-8, MR 1483118 Fresse, Benoit (2017), Homotopy of Operads and Grothendieck-Teichmüller Groups: Part 2: The Applications of (Rational)...

algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie operad Particle physics and representation theory Orthogonal symmetric Lie algebra...

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...

discussed in that article. See also Lie operad for the use of a free Lie algebra in the construction of the operad. Free object Free algebra Free group Berstel...

Eilenberg, Homological algebra Fresse, Benoit (21 April 2017). Homotopy of Operads and Grothendieck-Teichmuller Groups. Mathematical Surveys and Monographs...

Borcherds's later work on singular commutative rings, algebras over certain operads on curves introduced by Huang, Kriz, and others, D-module-theoretic objects...

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"...

conjecture about affine space.) In this line of the approach, the notion of operad, a set or space of operations, becomes prominent: in the introduction to...