2-Dimensional Categories
«This provides a highly useful resource for research mathematicians in various areas and graduate students alike. A clear benefit of this book is that often the data of a general definition are spelled out in detail.»
Robert Laugwitz, Mathematical Reviews Clippings
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. Les mer
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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.
Detaljer
- Forlag
- Oxford University Press
- Innbinding
- Innbundet
- Språk
- Engelsk
- ISBN
- 9780198871378
- Utgivelsesår
- 2021
- Format
- 4 x 16 cm
Anmeldelser
«This provides a highly useful resource for research mathematicians in various areas and graduate students alike. A clear benefit of this book is that often the data of a general definition are spelled out in detail.»
Robert Laugwitz, Mathematical Reviews Clippings
«This is a long-waited introduction to 2-categories and bicategories»
Hirokazu Nishimura, zbMATH Open