Rewriting in Operads and PROPs
نویسندگان
چکیده
منابع مشابه
Operads and Props
We review definitions and basic properties of operads, PROPs and algebras over these structures. Dedicated to the memory of Jakub Jan Ryba (1765–1815) Operads involve an abstraction of the family {Map(X, X)}n≥0 of composable functions of several variables together with an action of permutations of variables. As such, they were originally studied as a tool in homotopy theory, specifically for it...
متن کاملFrom Operads and Props to Feynman Processes
Operads and PROPs are presented, together with examples and applications to quantum physics suggesting the structure of Feynman categories/PROPs and the corresponding algebras.
متن کاملDiagram rewriting and operads
We introduce an explicit diagrammatic syntax for PROs and PROPs, which are used in the theory of operads. By means of diagram rewriting, we obtain presentations of PROs by generators and relations, and in some cases, we even get convergent rewrite systems. This diagrammatic syntax is useful for practical computations, but also for theoretical results. Moreover, rewriting is strongly related to ...
متن کاملAcademy of Sciences of the Czech Republic Mathematical Institute Operads and Props
We review definitions and basic properties of operads, PROPs and algebras over these structures. Dedicated to the memory of Jakub Jan Ryba (1765–1815) Operads involve an abstraction of the family {Map(X, X)}n≥0 of composable functions of several variables together with an action of permutations of variables. As such, they were originally studied as a tool in homotopy theory, specifically for it...
متن کاملKoszul Duality for PROPs
The notion of PROP models the operations with multiple inputs and multiple outputs, acting on some algebraic structures like the bialgebras or the Lie bialgebras. We prove a Koszul duality theory for PROPs generalizing the one for associative algebras and for operads.
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ژورنال
عنوان ژورنال: Journal of Non-linear Mathematical Physics
سال: 2006
ISSN: 1402-9251
DOI: 10.2991/jnmp.2006.13.supplement.8