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

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...

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...

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)...

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...

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

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

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...

}} , 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...

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...

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...

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...

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

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

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

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...

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

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...

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

"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...

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

following inclusions of full subcategories: O p e r a d s ⊂ 1 2 P R O P ⊂ P R O P {\displaystyle {\mathsf {Operads}}\subset {\tfrac {1}{2}}{\mathsf {PROP}}\subset...

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...

"Categorification". arXiv:math/9802029. Leinster, Tom (2004). Higher Operads, Higher Categories. Cambridge University Press. arXiv:math.CT/0305049....

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

Algebraic operads. Grundlehren der Mathematischen Wissenschaften. Vol. 346. Berlin: Springer-Verlag. p. 2. ISBN 978-3-642-30361-6. Zbl 1260.18001. v t e...