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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.

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