2-dimensional categories /
Johnson, Niles,
2-dimensional categories / Two-dimensional categories Niles Johnson, Donald Yau. - First edition. - New York, NY : Oxford University Press, 2021 - xix, 615 pages : illustrations ; 24 cm
Includes bibliographical references and index.
2--Dimensional Categories provides 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; the 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.--
9780198871378 9780198871385
2020947503
GBC0H5741 bnb
020006542 Uk
Categories (Mathematics)
QA169 / .J59 2021
512/.62 / J67
2-dimensional categories / Two-dimensional categories Niles Johnson, Donald Yau. - First edition. - New York, NY : Oxford University Press, 2021 - xix, 615 pages : illustrations ; 24 cm
Includes bibliographical references and index.
2--Dimensional Categories provides 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; the 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.--
9780198871378 9780198871385
2020947503
GBC0H5741 bnb
020006542 Uk
Categories (Mathematics)
QA169 / .J59 2021
512/.62 / J67