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Category Theory$
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Steve Awodey

Print publication date: 2006

Print ISBN-13: 9780198568612

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568612.001.0001

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(p.179) 9 ADJOINTS
Category Theory

Steve Awodey

Oxford University Press

This chapter focuses on notion of adjoint functor, which applies everything that has been learned so far to unify and subsume all the different universal mapping properties encountered, from free groups to limits to exponentials. It also captures an important mathematical phenomenon that is invisible without the use of the lens of category theory. It is argued that adjointness is a concept of fundamental logical and mathematical importance not captured elsewhere in mathematics. Topics discussed include hom-set definition, examples of adjoints, order adjoints, quantifiers as adjoints, RAPL 197, locally cartesian closed categories, and the adjoint functor theorem.

Keywords:   adjoint functor theorem, adjointness, hom-set definition, quantifiers, cartesian closed categories

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