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

(An operad that describes a multiplication that is both homotopy coherently associative and homotopy coherently commutative is called an E∞-operad.) In...

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...

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

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...

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 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...

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

commutative operad are commutative algebras, i.e., commutative (possibly graded, differential graded) rings. Yet another example is the Lie operad whose algebras...

v t e Mathematical logic General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory...

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

Numerical linear algebra Contents:  Top A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also References Operad theory a type of abstract algebra concerned...

is that A is an algebra in C over the little n-disks operad. An E n {\displaystyle {\mathcal {E}}_{n}} -algebra in vector spaces over a field is a unital...

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...

}} , called n {\displaystyle n} -box spaces, on which acts the planar operad, i.e. for any tangle T {\displaystyle T} (with one output disk and r {\displaystyle...

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...

S2CID 119168700. Sinha, Dev (2010-02-20). "The homology of the little disks operad". p. 2. arXiv:math/0610236. Magnus, Wilhelm (1974). "Braid groups: A survey"...

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

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

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

of a cactus operad on the free loop space L M {\displaystyle LM} . The cactus operad is weakly equivalent to the framed little disks operad and its action...

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

to non-mathematicians." Spivak has also studied dynamical systems and operads, originating the operadic approach to wiring diagram syntax. His unpublished...

only finitely many cells in each dimension. operad The portmanteau of “operations” and “monad”. See operad. orbibundle orbibundle. orbit category orientation...

"colored operad" is more primitive than that of operad: in fact, an operad can be defined as a colored operad with a single object. comma Given functors f...

geometry - Rezk Operads and Sheaf Cohomology - JP May - E ∞ {\displaystyle E_{\infty }} -rings over characteristic 0 and E ∞ {\displaystyle E_{\infty }} -structure...

of algebra for T, that satisfies the laws up to coherent isomorphisms. Operad Shulman, Michael A. (2012). "Not every pseudoalgebra is equivalent to a...