2-Dimensional Categories
Kiadó: OUP Oxford
Megjelenés dátuma: 2021. január 31.
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GBP 110.00
GBP 110.00
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47 817 (45 540 Ft + 5% áfa )
Kedvezmény(ek): 10% (kb. 5 313 Ft)
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A termék adatai:
| ISBN13: | 9780198871378 |
| ISBN10: | 0198871376 |
| Kötéstípus: | Keménykötés |
| Terjedelem: | 636 oldal |
| Méret: | 38x160x241 mm |
| Súly: | 1184 g |
| Nyelv: | angol |
| 284 |
Témakör:
Rövid leírás:
2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
Hosszú leírás:
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.
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.
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.
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.
Tartalomjegyzék:
Categories
2-Categories and Bicategories
Pasting Diagrams
Functors, Transformations, and Modifications
Bicategorical Limits and Nerves
Adjunctions and Monads
The Whitehead Theorem for Bicategories
The Yoneda Lemma and Coherence
Grothendieck Fibrations
The Grothendieck Construction
The Tricategory of Bicategories
Further 2-Dimensional Categorical Structures
2-Categories and Bicategories
Pasting Diagrams
Functors, Transformations, and Modifications
Bicategorical Limits and Nerves
Adjunctions and Monads
The Whitehead Theorem for Bicategories
The Yoneda Lemma and Coherence
Grothendieck Fibrations
The Grothendieck Construction
The Tricategory of Bicategories
Further 2-Dimensional Categorical Structures
