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Minimal models for graph-related (hyper)operads
Institution:1. Mathematical Institute, The Czech Academy of Sciences, ?itná 25, 115 67 Prague 1, the Czech Republic;2. Mathematical Institute SANU, Knez Mihailova 36, p.f. 367, 11001 Belgrade, Serbia;1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, PR China;2. Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan, 430074, PR China;3. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, PR China;1. Department of Mathematics, Middle East Technical University, Ankara, Turkey;2. Department of Mathematics, Do?u? University, Istanbul, Turkey;1. Department of Mathematics, Yaroslavl P. Demidov State University, Sovetskaya Str. 14, 150000 Yaroslavl, Russia;2. Escuela Técnica Superior de Ingeniería Informática, Instituto Universitario de Matemática Pura y Aplicada, IUMPA-UPV, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain;3. Departament d?Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot (València), Spain
Abstract:We construct explicit minimal models for the (hyper)operads governing modular, cyclic and ordinary operads, and wheeled properads, respectively. Algebras for these models are homotopy versions of the corresponding structures.
Keywords:Operad  Operadic category  Hypergraph  Polyhedral realization  Minimal model  Cooperative game
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