This monograph presents a new model of mathematical structures called weak n-categories. These
structures find their motivation in a wide range of fields from algebraic topology to
mathematical physics algebraic geometry and mathematical logic.While strict n-categories are
easily defined in terms associative and unital composition operations they are of limited use
in applications which often call for weakened variants of these laws. The author proposes a
new approach to this weakening whose generality arises not from a weakening of such laws but
from the very geometric structure of its cells a geometry dubbed weak globularity. The new
model called weakly globular n-fold categories is one of the simplest known algebraic
structures yielding a model of weak n-categories. The central result is the equivalence of this
model to one of the existing models due to Tamsamani and further studied by Simpson. This
theory has intended applications to homotopy theory mathematical physics and to long-standing
open questions in category theory.As the theory is described in elementary terms and the book
is largely self-contained it is accessible to beginning graduate students and to
mathematicians from a wide range of disciplines well beyond higher category theory. The new
model makes a transparent connection between higher category theory and homotopy theory
rendering it particularly suitable for category theorists and algebraic topologists. Although
the results are complex readers are guided with an intuitive explanation before each concept
is introduced and with diagrams showing the interconnections between the main ideas and
results.
