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Simplicial Methods for Higher Categories - Segal-type Models of Weak n-Categories (Hardcover, 1st ed. 2019)
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Simplicial Methods for Higher Categories - Segal-type Models of Weak n-Categories (Hardcover, 1st ed. 2019)
Series: Algebra and Applications, 26
Expected to ship within 10 - 15 working days
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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.
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