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CATEGORIES OF DIAGRAMS

Steve Awodey

in Category Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.003.0008
Subject:
Mathematics, Algebra

This chapter presents the proof for the Yoneda Lemma, which is probably the single most used result in category theory. It is interesting how often it comes up, especially in view of the fact that it ... More


The Yoneda Lemma and Coherence

Niles Johnson and Donald Yau

in 2-Dimensional Categories

Published in print:
2021
Published Online:
February 2021
ISBN:
9780198871378
eISBN:
9780191914850
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198871378.003.0008
Subject:
Mathematics, Geometry / Topology

In this chapter, the Yoneda Lemma and the Coherence Theorem for bicategories are stated and proved. The chapter discusses the bicategorical Yoneda pseudofunctor, a bicategorical version of the Yoneda ... More


Categories

Niles Johnson and Donald Yau

in 2-Dimensional Categories

Published in print:
2021
Published Online:
February 2021
ISBN:
9780198871378
eISBN:
9780191914850
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198871378.003.0001
Subject:
Mathematics, Geometry / Topology

In this chapter, categories are defined, and basic concepts are reviewed. Starting from the definitions of a category, a functor, and a natural transformation, the chapter reviews limits, ... More


2-Dimensional Categories

Niles Johnson and Donald Yau

Published in print:
2021
Published Online:
February 2021
ISBN:
9780198871378
eISBN:
9780191914850
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198871378.001.0001
Subject:
Mathematics, Geometry / Topology

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 ... More


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