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Generalization of associativity properties
operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification
Operad
In mathematics, an A∞-operad is a type of operad used in algebraic topology and homotopy theory to describe algebraic structures where the property of
A∞-operad
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
Operad_algebra
Infinite loop space
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
E∞-operad
Various mathematical dualites
who 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
Koszul_duality
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)
Lie_operad
Cohomology class
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
Highly structured ring spectrum
Highly_structured_ring_spectrum
American mathematician (born 1939)
sequence and for coining the term operad. May received a Bachelor of Arts degree from Swarthmore College in 1960 and a Doctor of Philosophy degree from
J._Peter_May
Sum of terms, each multiplied with a scalar
the most general sort of operation on a vector space – saying that a vector space is an algebra over the operad of linear combinations is precisely the
Linear_combination
Russian-American mathematician
topology (see cactus operad). He is a Fellow of the American Mathematical Society, an AMS Centennial Fellow,, a Simons Fellow, and a 2010 Japan Society
Alexander_A._Voronov
Generalization of the concept of category that allows morphisms of multiple arity
morphisms in a multicategory are analogous to functions of several variables. Multicategories are also sometimes called operads, or colored operads. A (non-symmetric)
Multicategory
(colored symmetric) operads, also called symmetric multicategories, that simplicial sets have to categories. A dendroidal set is a contravariant functor
Dendroidal_set
Mathematical operation with two operands
mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary
Binary_operation
Vector space equipped with a bilinear product
element for a description of an attempt to give to every ring a structure that behaves like an algebra over a field. Algebra over an operad Alternative
Algebra_over_a_field
geometry; supersymmetry; operads; and Hopf algebras. He retired in 2014. A 2002 book of Markl, Shnider and Stasheff Operads in algebra, topology, and
Steve_Shnider
Theory of algebraic structures in general
of a large class of categories (namely those having finite products). A more recent development in category theory is operad theory – an operad is a set
Universal_algebra
Type of monoidal category in category theory
Rainer Vogt. Following them, J. P. May then introduced the term “operad”, which is a particular kind of PROP, for the object that Boardman and Vogt called
PROP_(category_theory)
be defined as a colored operad or multicategory. In particular, a pseudo-tensor category with a single object is the same as an operad. A pseudo-tensor
Pseudo-tensor_category
Operation in algebra and mathematics
monads, monoidal approach to bicategorical structures and generalized operads". Theory and Applications of Categories. 30: 332–386. doi:10.70930/tac/nfe2xf1p
Monad_(category_theory)
American mathematician
San Diego. His research concerns topology and geometry, mostly seen through a discrete and computational lens, with inspiration coming from theoretical
Satyan_Devadoss
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
Planar_algebra
exists a more abstract definition of a homotopy algebra using the theory of operads: that is, a homotopy Lie algebra is an algebra over an operad in the
Homotopy_Lie_algebra
Algebraic structure used in analysis
Index of a Lie algebra Leibniz algebra Lie algebra cohomology Lie algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie operad Particle
Lie_algebra
General theory of mathematical structures
Mathematics: A First Introduction to Categories (2nd ed.). Cambridge University Press. ISBN 978-0-521-89485-2. Leinster, Tom (2004). Higher Operads, Higher
Category_theory
Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and the Deligne conjecture". Conférence Moshé Flato 1999, Vol. I (Dijon)
Deligne's conjecture on Hochschild cohomology
Deligne's_conjecture_on_Hochschild_cohomology
Type of mathematical category
equivalent as a category to the category of finite sets and bijections between them. Trimble n.d., § 1 Trimble, Todd H. "Notes on the Lie operad" (PDF). University
Permutation_category
Concept in mathematics
(2010-02-20). "The homology of the little disks operad". p. 2. arXiv:math/0610236. Magnus, Wilhelm (1974). "Braid groups: A survey". Proceedings of the Second International
Configuration space (mathematics)
Configuration_space_(mathematics)
Polytope of operations
define a weak n-category as a certain presheaf on the category of opetopes. higher-order operad Leinster, Tom (2004). "Opetopes". Higher Operads, Higher
Opetope
Branch of topology
action 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
String_topology
Operation in graph theory
Sistemy, 9: 30–43, MR 0209178. Weber, Mark (2013), "Free products of higher operad algebras", Theory and Applications of Categories, 28 (2): 24–65. Weisstein
Cartesian_product_of_graphs
Russian mathematician (born 1962)
algebraic surfaces. In 1998 Kapranov was an Invited Speaker with talk Operads and Algebraic Geometry at the International Congress of Mathematicians
Mikhail_Kapranov
Mathematical condition
Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and Deligne's conjecture". Conférence Moshé Flato 1999: Quantization, Deformations
Poincaré_lemma
American mathematician
International Congress of Mathematicians. Vol. 2. pp. 433–442. "Introduction to Operads (William Dwyer @ MSRI)". YouTube. 5 August 2014. (See operad.)
William_Gerard_Dwyer
Mathematician
graduated in 2000 with a PhD from the University of Cambridge. His PhD thesis Operads in Higher-Dimensional Category Theory was supervised by Martin Hyland.
Tom_Leinster
195–213. Ginzburg, Victor; Kapranov, Mikhail (1994). "Koszul duality for operads". Duke Mathematical Journal. 76: 203–273. arXiv:0709.1228. doi:10
Zinbiel_algebra
of a link group are related to the free Lie algebra on the components of the link, as discussed in that article. See also Lie operad for the use of a free
Free_Lie_algebra
Symmetric monoidal infinity category
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
En-ring
Algebra used in 2D conformal field theories and string theory
Borcherds's later work on singular commutative rings, algebras over certain operads on curves introduced by Huang, Kriz, and others, D-module-theoretic objects
Vertex_operator_algebra
Bosnian-American mathematician
Mathematical Social Sciences, 114 (2021), 39–57 "Formality of the little N-discs operad", with P. Lambrechts, Memoirs of the American Mathematical Society, 239
Ismar_Volić
Mathematical group
ISBN 978-0-521-59642-8, MR 1483118 Fresse, Benoit (2017), Homotopy of Operads and Grothendieck-Teichmüller Groups: Part 2: The Applications of (Rational)
Grothendieck–Teichmüller group
Grothendieck–Teichmüller_group
Convex polytope of parenthesizations
Foundation. Holtkamp, Ralf (2006), "On Hopf algebra structures over free operads", Advances in Mathematics, 207 (2): 544–565, arXiv:math/0407074, doi:10
Associahedron
Topics referred to by the same term
ring, a commutative ring construct in homotopy theory E∞-operad, a set of contractible maps that are commutative and associative E-infinity theory, a fringe
E∞
Mathematics glossary
“monad”. See operad. orbibundle orbibundle. orbit category orientation 1. The orientation covering (or orientation double cover) of a manifold is a two-sheeted
Glossary of algebraic topology
Glossary_of_algebraic_topology
American mathematician
to non-mathematicians." Spivak has also studied dynamical systems and operads, originating the operadic approach to wiring diagram syntax. His unpublished
David_Spivak
Number in combinatorics
Studies in Ancient Philosophy, XL: 157–188. Weisstein, Eric W., "Super Catalan Number", MathWorld The Hipparchus Operad, The n-Category Café, April 1, 2013
Schröder–Hipparchus_number
Branch of mathematics
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
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
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
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Mathematical concept
Eilenberg, Homological algebra Fresse, Benoit (21 April 2017). Homotopy of Operads and Grothendieck-Teichmuller Groups. Mathematical Surveys and Monographs
Differential_graded_module
Mathematical framework for knowledge representation
Ontology language Operad theory Orgology Universal algebra Universal logic Spivak, David I.; Kent, Robert E. (31 January 2012). "Ologs: A Categorical Framework
Olog
2-category version of algebra
the laws up to coherent isomorphisms. Operad Shulman, Michael A. (2012). "Not every pseudoalgebra is equivalent to a strict one". Advances in Mathematics
Pseudoalgebra
(2003-10-21), Sur les A-infini catégories, arXiv:math/0310337, Bibcode:2003math.....10337L Vallette, Bruno (2012-02-15). "Algebra+Homotopy=Operad". arXiv:1202
Homotopy_associative_algebra
Chapoton, F.; Livernet, M. (2001), "Pre-Lie algebras and the rooted trees operad", International Mathematics Research Notices, 2001 (8): 395–408, arXiv:math/0002069
Pre-Lie_algebra
French mathematician (1946–2012)
S2CID 16865683. Loday, Jean-Louis; Vallette, Bruno (2012), Algebraic Operads (PDF), Grundlehren der Mathematischen Wissenschaften, vol. 346, Berlin
Jean-Louis_Loday
History of maths
21, 1996). "The Pre-History Of Operads". In Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.). Operads: Proceedings of Renaissance Conferences
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
French mathematician (1924–1987)
(Lazard's universal ring) is a polynomial ring. The concept of "analyseurs", reinvented by J. Peter May under the name operads. In 1958, Lazard was the first
Michel_Lazard
S2CID 121944962. Ginzburg, V.; Kapranov, M. (1994). "Koszul duality for operads". Duke Math. J. 76: 203–273. arXiv:0709.1228. doi:10.1215/s0012-7094-94-07608-4
Leibniz_algebra
Generalization of category theory
"Categorification". arXiv:math/9802029. Leinster, Tom (2004). Higher Operads, Higher Categories. Cambridge University Press. arXiv:math.CT/0305049.
Higher_category_theory
Standard that diagrams must satisfy up to isomorphism
Différentielle Catégoriques. 41 (4): 255–304. Leinster, Tom (22 July 2004). Higher Operads, Higher Categories. Cambridge University Press. ISBN 978-0-521-53215-0
Coherency_(homotopy_theory)
Russian American mathematician (born 1957)
Furthermore, Ginzburg and Mikhail Kapranov developed Koszul duality theory for operads. In noncommutative geometry, Ginzburg defined, following earlier ideas
Victor_Ginzburg
"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 : C
Glossary_of_category_theory
American mathematician
associahedron (also called the Stasheff polytope), ideas leading to the theory of operads; homotopy theoretic approaches to Hilbert's fifth problem on the characterization
Jim_Stasheff
Opera company based in New York City
Age. April 30, 1955. p. 19. "Strauss Created New Orchestra in Writing His Operad Ariadne". Montreal Gazette. November 26, 1946. Rebecca Paller (October 12
New_York_City_Opera
Branch of mathematics
commutative ring Derivator Algebra over an operad En-ring Higher Topos Theory ∞-topos étale spectrum Khan, Adeel A. (2019). "Brave new motivic homotopy theory
Derived_algebraic_geometry
Concept in universal algebra in mathematics
elements of (Cm)n. This induces a bijective correspondence between Lawvere theories and abstract clones. Term algebra Operad Denecke, Klaus (2003). "Menger
Clone_(algebra)
Algebraic structure in homological algebra
Deformation Theory. I (PDF) Loday, Jean-Louis; Vallette, Bruno (2012), Algebraic Operads, Grundlehren der mathematischen Wissenschaften, vol. 346, Heidelberg, New
Differential_graded_algebra
Frabetti, Alessandra; Goichot, François (eds.). Dialgebras and Related Operads. Lecture Notes in Mathematics. Vol. 1763. Springer. pp. 7–66. doi:10.1007/3-540-45328-8_2
Dialgebra
Alternative mathematical ordering
(1997), "From operads to 'physically' inspired theories", in Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.), Operads: Proceedings
Cyclic_order
American mathematician
1991 with B.A. and M.A. in mathematics. In 1996 he received his PhD from MIT with thesis Spaces of Algebra Structures and Cohomology of Operads and advisor
Charles_Rezk
see the introduction of Lurie's paper, leading to the notion of an operad.) Given a based space ( X , ∗ ) {\displaystyle (X,*)} , we let P ′ X = { f :
Path_space_fibration
Process in mathematics
337–350, MR 1767430. Loday, Jean-Louis; Vallette, Bruno (2012), Algebraic operads (PDF), Grundlehren der Mathematischen Wissenschaften [Fundamental Principles
Koszul_algebra
Getzler & Jones 1994, § 1 Getzler, Ezra; Jones, J. D. S. (1994-03-08). "Operads, homotopy algebra and iterated integrals for double loop spaces". arXiv:hep-th/9403055
S-object
Dutch mathematician
the theory of operads, on the logic structure of quantum information theory, and on dendroidal sets. Moerdijk has written more than a hundred publications
Ieke_Moerdijk
Polytope associated with combinatorial problems
"A type-B associahedron". Advances in Applied Mathematics. 30 (1–2): 2–25. doi:10.1016/S0196-8858(02)00522-5. Stasheff, Jim (1997), "From operads to
Cyclohedron
Kazakh mathematician and physicist (born 1956)
Dzhumadildaev A.S., Codimension growth and non-Koszulity of Novikov operad // Communications in Algebra. – 2011. – V. 39, No.8. – P. 2943–2952. Dzhumadildaev A.S
Askar_Dzhumadildayev
Theorem in category theory
ISSN 1076-9803. Loday, Jean-Louis; Vallette, Bruno (8 August 2012). Algebraic Operads. Grundlehren der mathematischen Wissenschaften. Vol. 346. Springer. doi:10
Mac_Lane's_coherence_theorem
{\displaystyle k[x]} . Loday, Jean-Louis; Vallette, Bruno (2012). Algebraic operads. Grundlehren der Mathematischen Wissenschaften. Vol. 346. Berlin: Springer-Verlag
Augmentation_(algebra)
1999). "Operads and Motives in Deformation Quantization". Letters in Mathematical Physics. 48 (1): 35–72. arXiv:math/9904055. doi:10.1023/A:1007555725247
Deformation_quantization
German mathematician
topology, invented by Moira Chas and Dennis Sullivan, and operad theory. Here he first proved a cyclic version of Pierre Deligne's conjecture in deformation
Ralph_Kaufmann
Generalization of a semialgebraic set
S2CID 50187913. Maxim Kontsevich and Yan Soibelman. “Deformations of algebras over operads and the Deligne conjecture”. In: Conférence Moshé Flato 1999, Vol. I (Dijon)
Piecewise_algebraic_space
Mathematical structures in category theory
morphisms is therefore a cartesian closed category. Mathematics portal Diagram (category theory) Tom Leinster (2004). Higher Operads, Higher Categories.
Functor_category
American mathematician and novelist
"Grothendieck–Teichmüller groups", Grothendieck–Teichmüller Groups, Deformation and Operads, archived from the original on 2014-03-09, retrieved 2014-01-02 Schneps
Leila_Schneps
Higher category theory concept
ISBN 978-1-4419-1523-8. Leinster, Tom (2001). "A Survey of Definitions of n-Category". arXiv:math/0107188. Leinster, Tom (2004a). "Operads in Higher-Dimensional Category
Weak_n-category
(under construction) Lecture 4 of Part II of Moerdijk-Toen, Simplicial Methods for Operads and Algebraic Geometry Ch. 2.2. of Toen-Vezzosi's HAG II v t e
Derived_tensor_product
Graduate-level textbooks in mathematics
Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). The
Graduate Studies in Mathematics
Graduate_Studies_in_Mathematics
Gröbner bases for non-commutative algebra
Hecke algebras. For category algebras. For small categories. For shuffle operads. The lemma has been used to prove the Poincaré–Birkhoff–Witt theorem. Rogalski
Bergman's_diamond_lemma
Mathematician
(2020), whose dissertation was entitled Symmetric Homotopy Theory for Operads and Weak Lie 3-Algebras, Du Li (2014), whose dissertation was entitled
Chenchang_Zhu
F.; Markl, M. (1997). "Distributive laws, bialgebras, and cohomology". Operads: Proceedings of Renaissance Conferences. Contemporary Mathematics. Vol
Distributive law between monads
Distributive_law_between_monads
Belgian mathematician
journal paper. She completed a Ph.D. at the University of Oxford in 2001, with a dissertation Ribbon Graphs and Related Operads in algebraic topology supervised
Nathalie_Wahl
A OPERAD
A OPERAD
Female
Polish
Feminine form of Polish BogumiÅ‚, BOGUMIÅA means "God-favor."
Female
Spanish
Spanish form of Greek Sophia, SOFÃA means "wisdom."
Male
Thai/Siamese
Thai name A-WUT means "weapon."
Female
Icelandic
Icelandic form of Old Norse Gerðr, GERÃA means "enclosure, stronghold."
Female
Swedish
Short form of Swedish Linnéa, NÉA means "twinflower."
Female
Polish
Feminine form of Polish RadomiÅ‚, RADOMIÅA means "happy favor."
Female
Spanish
Feminine form of Spanish Estéban, ESTEFANÃA means "crown."
Female
Thai/Siamese
Thai name A-GUN means "grape."
Female
Spanish
Spanish form of Roman Latin Lucia, LUCÃA means "light."Â
Female
Swedish
Swedish form of Latin Linnaea, LINNÉA means "twin flower."
Female
French
French form of Hebrew Leah, LÉA means "weary."
Female
Slovene
Feminine form of Slovene Sašo, SAŠA means "defender of mankind."
Female
Portuguese
Galician-Portuguese form of Hebrew Leah, LÃA means "weary."
Female
Egyptian
, a royal lady of the IIIrd or IVth dynasty.
Female
Portuguese
Portuguese name GRAÇA means "graceful."
Female
Slovene
Slovene form of Greek Hagne, NEŽA means "chaste; holy."
Female
Polish
Feminine form of Polish LudmiÅ‚, LUDMIÅA means "people's favor."
Female
Spanish
Feminine form of Spanish PÃo, PÃA means "pious."
Female
Icelandic
Feminine form of Icelandic Stefán, STEFANÃA means "crown."
Female
Portuguese
Feminine form of Galician-Portuguese UxÃo, UXÃA means "well born."
A OPERAD
A OPERAD
Boy/Male
African, American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Jamaican, Swedish
Ruler of the People; Form of Derek; Ruler; People's Ruler; First of the People; King of Nations
Girl/Female
Hindu, Indian, Marathi, Tamil
Well Minded; Thoughtful
Surname or Lastname
English
English : variant of Boniface.
Girl/Female
Hindu
Sarovar, Type of Shakti
Boy/Male
Hindu, Indian, Mythological
Kartikeya; First Son of Lord Shiva
Boy/Male
Teutonic
Famous fighter.
Boy/Male
Hindu
Boy/Male
Indian, Tamil
Lord of Krishna
Girl/Female
Indian
Pure as water, Pearl
Girl/Female
Christian & English(British/American/Australian)
Feminine of Adrian
A OPERAD
A OPERAD
A OPERAD
A OPERAD
A OPERAD
a.
Private; confidential; familiar.
prep.
In; on; at; by.
n.
A thin gelatinous tissue separating the ectoderm and endoderm in certain coelenterates.
a.
Dark-visaged; swart.
n.
A flow or running from the ear, esp. a purulent discharge.
a.
Boastful; defiant; exulting. Also used adverbially.
a.
See Alamort.
prep.
In process of; in the act of; into; to; -- used with verbal substantives in -ing which begin with a consonant. This is a shortened form of the preposition an (which was used before the vowel sound); as in a hunting, a building, a begging.