Add to ORKGOperads are objects that model operations with several inputs and one output. We define such structures in the context of graphs, namely oriented trees. Then we generalize operads to properads and modular operads by taking general graphs with, or without, orientation. Further we construct the cobar complex of operads and properads and illustrate the construction on the examples of the associative operad Ass and the Frobenius properad Frob. Algebras over the cobar complex of operads correspond to certain homotopy algebras, for our example of Ass it is A1. We find its Maurer-Cartan equation and convert it from coderivations to derivations. Similarly we find the Maurer-Cartan equation for cobar complex of Frobenius properad. Powered by TCPDF (...
Abstract. We complete a certain diagram (the operadic butterfly) of the categories of algebras invol...
summary:We give a biased definition of a properad and an explicit example of a closed Frobenius prop...
38 pagesInternational audienceWe extend the bar-cobar adjunction to operads and properads, not neces...
Operads are objects that model operations with several inputs and one output. We define such structu...
summary:We give a biased definition of a properad and an explicit example of a closed Frobenius prop...
summary:We give a biased definition of a properad and an explicit example of a closed Frobenius prop...
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (s...
International audienceWe introduce a functorial construction which, from a monoid, produces a set-op...
85 pagesWe study different algebraic structures associated to an operad and their relations: to any ...
This thesis deals with the homotopical properties of algebras over an operad, of operads themselves ...
This thesis deals with the homotopical properties of algebras over an operad, of operads themselves ...
This thesis deals with the homotopical properties of algebras over an operad, of operads themselves ...
59 figures, 31 exercices, 43 pages. To appear in the proceedings of the MSRI and RIMS "Symplectic Ge...
Wiring diagrams form a kind of graphical language that describes operations or processes with multip...
The notion of an operad supplies both a conceptual and effective device to handle a variety of algeb...
Abstract. We complete a certain diagram (the operadic butterfly) of the categories of algebras invol...
summary:We give a biased definition of a properad and an explicit example of a closed Frobenius prop...
38 pagesInternational audienceWe extend the bar-cobar adjunction to operads and properads, not neces...
Operads are objects that model operations with several inputs and one output. We define such structu...
summary:We give a biased definition of a properad and an explicit example of a closed Frobenius prop...
summary:We give a biased definition of a properad and an explicit example of a closed Frobenius prop...
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (s...
International audienceWe introduce a functorial construction which, from a monoid, produces a set-op...
85 pagesWe study different algebraic structures associated to an operad and their relations: to any ...
This thesis deals with the homotopical properties of algebras over an operad, of operads themselves ...
This thesis deals with the homotopical properties of algebras over an operad, of operads themselves ...
This thesis deals with the homotopical properties of algebras over an operad, of operads themselves ...
59 figures, 31 exercices, 43 pages. To appear in the proceedings of the MSRI and RIMS "Symplectic Ge...
Wiring diagrams form a kind of graphical language that describes operations or processes with multip...
The notion of an operad supplies both a conceptual and effective device to handle a variety of algeb...
Abstract. We complete a certain diagram (the operadic butterfly) of the categories of algebras invol...
summary:We give a biased definition of a properad and an explicit example of a closed Frobenius prop...
38 pagesInternational audienceWe extend the bar-cobar adjunction to operads and properads, not neces...