Coherence in Three-Dimensional Category Theory

Higher category theory is an increasingly important discipline with applications in topology, geometry, logic and theoretical computer science. This comprehensive treatment covers essential material for any student of coherence, or for any researcher wishing to apply higher categories or coherence results in fields such as algebraic topology.

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Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science.