The subject of this book is the theory of operads and colored
operads, sometimes called symmetric multicategories. A (colored)
operad is an abstract object which encodes operations with multiple
inputs and one output and relations between such operations. The
theory originated in the early 1970s in homotopy theory and quickly
became very important in algebraic topology, algebra, algebraic
geometry, and even theoretical physics (string theory). Topics
covered include basic graph theory, basic category theory, colored
operads, and algebras over colored operads. Free colored operads
are discussed in complete detail and in full generality. The
intended audience of this book includes students and researchers in
mathematics and other sciences where operads and colored operads
are used. The prerequisite for this book is minimal. Every major
concept is thoroughly motivated. There are many graphical
illustrations and about 150 exercises. This book can be used in a
graduate course and for independent study.
General
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