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Books > Computing & IT > General theory of computing
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2-Dimensional Categories (Paperback)
Loot Price: R2,187
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2-Dimensional Categories (Paperback)
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Category theory emerged in the 1940s in the work of Samuel
Eilenberg and Saunders Mac Lane. It describes relationships between
mathematical structures. Outside of pure mathematics, category
theory is an important tool in physics, computer science,
linguistics, and a quickly-growing list of other sciences. This
book is about 2-dimensional categories, which add an extra
dimension of richness and complexity to category theory.
2-Dimensional Categories is an introduction to 2-categories and
bicategories, assuming only the most elementary aspects of category
theory. A review of basic category theory is followed by a
systematic discussion of 2-/bicategories, pasting diagrams, lax
functors, 2-/bilimits, the Duskin nerve, 2-nerve, internal
adjunctions, monads in bicategories, 2-monads, biequivalences, the
Bicategorical Yoneda Lemma, and the Coherence Theorem for
bicategories. Grothendieck fibrations and the Grothendieck
construction are discussed next, followed by tricategories,
monoidal bicategories, the Gray tensor product, and double
categories. Completely detailed proofs of several fundamental but
hard-to-find results are presented for the first time. With
exercises and plenty of motivation and explanation, this book is
useful for both beginners and experts.
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