This open access book offers a self-contained introduction to the
homotopy theory of simplicial and dendroidal sets and spaces. These
are essential for the study of categories, operads, and algebraic
structure up to coherent homotopy. The dendroidal theory combines
the combinatorics of trees with the theory of Quillen model
categories. Dendroidal sets are a natural generalization of
simplicial sets from the point of view of operads. In this book,
the simplicial approach to higher category theory is generalized to
a dendroidal approach to higher operad theory. This dendroidal
theory of higher operads is carefully developed in this book. The
book also provides an original account of the more established
simplicial approach to infinity-categories, which is developed in
parallel to the dendroidal theory to emphasize the similarities and
differences. Simplicial and Dendroidal Homotopy Theory is a
complete introduction, carefully written with the beginning
researcher in mind and ideally suited for seminars and courses. It
can also be used as a standalone introduction to simplicial
homotopy theory and to the theory of infinity-categories, or a
standalone introduction to the theory of Quillen model categories
and Bousfield localization.
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