At the heart of this short introduction to category theory is the
idea of a universal property, important throughout mathematics.
After an introductory chapter giving the basic definitions,
separate chapters explain three ways of expressing universal
properties: via adjoint functors, representable functors, and
limits. A final chapter ties all three together. The book is
suitable for use in courses or for independent study. Assuming
relatively little mathematical background, it is ideal for
beginning graduate students or advanced undergraduates learning
category theory for the first time. For each new categorical
concept, a generous supply of examples is provided, taken from
different parts of mathematics. At points where the leap in
abstraction is particularly great (such as the Yoneda lemma), the
reader will find careful and extensive explanations. Copious
exercises are included.
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