An array of general ideas useful in a wide variety of fields. Starting
from the foundations, this book illuminates the concepts of category,
functor, natural transformation, and duality. It then turns to adjoint
functors, which provide a description of universal constructions, an
analysis of the representations of functors by sets of morphisms, and a
means of manipulating direct and inverse limits. These categorical
concepts are extensively illustrated in the remaining chapters, which
include many applications of the basic existence theorem for adjoint
functors. The categories of algebraic systems are constructed from
certain adjoint-like data and characterised by Beck's theorem. After
considering a variety of applications, the book continues with the
construction and exploitation of Kan extensions. This second edition
includes a number of revisions and additions, including new chapters on
topics of active interest: symmetric monoidal categories and braided
monoidal categories, and the coherence theorems for them, as well as
2-categories and the higher dimensional categories which have recently
come into prominenceDownload
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