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UBC Theses and Dissertations
Adjunctions and monads in categories and 2-categories Gilbride, E. A. Bridget
Abstract
The study of 2-categories extends many of the constructions within category theory itself. In particular, this thesis investigates the important categorical constructions of an adjunction and a monad within the context of a 2-category. Chapter 1 introduces the fundamental notions of category theory, with an emphasis on presenting a wide variety of examples. It is a goal of this chapter that a reader unfamiliar with category theory is provided with sufficient background to follow subsequent chapters, as well as gain an appreciation for the power of category theory throughout mathematics. "The slogan is: 'Adjoints arise everywhere'," writes Saunders MacLane, one of the founders of Category Theory, in the preface to his book Categories for the Working Mathematician. Chapter 2 begins by defining the concept of adjoint functors; the second focus of this chapter is that of a monad. The relationship between these two is then discussed in detail. The notion of 2-categories is defined in Chapter 3. We go on to extrapolate many of the categorical structures discussed in Chapters 1 and 2 to 2-categorical structures.
Item Metadata
| Title |
Adjunctions and monads in categories and 2-categories
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| Creator | |
| Publisher |
University of British Columbia
|
| Date Issued |
2003
|
| Description |
The study of 2-categories extends many of the constructions within category
theory itself. In particular, this thesis investigates the important categorical constructions
of an adjunction and a monad within the context of a 2-category.
Chapter 1 introduces the fundamental notions of category theory, with an emphasis
on presenting a wide variety of examples. It is a goal of this chapter that
a reader unfamiliar with category theory is provided with sufficient background
to follow subsequent chapters, as well as gain an appreciation for the power of
category theory throughout mathematics.
"The slogan is: 'Adjoints arise everywhere'," writes Saunders MacLane, one of
the founders of Category Theory, in the preface to his book Categories for the
Working Mathematician. Chapter 2 begins by defining the concept of adjoint
functors; the second focus of this chapter is that of a monad. The relationship
between these two is then discussed in detail.
The notion of 2-categories is defined in Chapter 3. We go on to extrapolate
many of the categorical structures discussed in Chapters 1 and 2 to 2-categorical
structures.
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| Extent |
1970155 bytes
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| Genre | |
| Type | |
| File Format |
application/pdf
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| Language |
eng
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| Date Available |
2009-11-14
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0080042
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2004-05
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.