Colored operads (Q2801244)

This book is a useful introduction to colored operads or symmetric muticategories, to the destination of students as well as researchers interested in these objects. An important emphasis is put on motivations, graphical representations and exercises (about 150, of various levels), all written in mind of a broad audience. It is decomposed into four parts.NEWLINENEWLINEThe first part (6 chapters) introduces some notions of graph theory: graphs, rooted trees, and various operations on them, such as graftings or edge collapsings. The second part (3 chapters) is devoted to categories, and to related notions such as functors, natural transformations, symmetric monoidal categories. The aim of this two first parts is to give all the tools which will be needed in the sequel.NEWLINENEWLINEIn the third part (7 chapters), after a chapter of motivations, the axioms of colored operads in a symmetric monoidal category are given. Algebras over colored operads are then introduced, as well as examples. This part ends with the notion of partial composition -- a way of reformulating the axioms of colored operads, and with colored pseudo-operads.NEWLINENEWLINEIn the last part (4 chapters), free colored operads are described, in the non-symmetric context first, after some motivations and the introduction of the general operadic composition.