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Within the past ten years, category theory has become
an import avenue of research in computer science.
This book explores some categorical ideas introduced
by B. Jacobs and J. Rutten in "A tutorial on
(co)algebras and (co)induction" [EATCS Bulletin,
62(222-259):3-13, 1997]. From foundational sets and
functions, we gradually build up to definitions of
functors and diagrams. Then, we define algebras and
coalgebras and prove some properties used in the next
section, where we show by examples how the
categorical ideas are implemented in the programming
language Charity. Exercises are sprinkled throughout
the first chapter to reinforce understanding. The
prerequisites for this book are basic intuitions and
notational knowledge for sets and functions; no
understanding of Charity is assumed. As such, this
work should be useful to anyone interested in
category theory that finds programming to be a useful
tool in understanding abstract ideas. In addition,
as an introductory work, this book should prepare the
reader for more advanced literature in the field.
an import avenue of research in computer science.
This book explores some categorical ideas introduced
by B. Jacobs and J. Rutten in "A tutorial on
(co)algebras and (co)induction" [EATCS Bulletin,
62(222-259):3-13, 1997]. From foundational sets and
functions, we gradually build up to definitions of
functors and diagrams. Then, we define algebras and
coalgebras and prove some properties used in the next
section, where we show by examples how the
categorical ideas are implemented in the programming
language Charity. Exercises are sprinkled throughout
the first chapter to reinforce understanding. The
prerequisites for this book are basic intuitions and
notational knowledge for sets and functions; no
understanding of Charity is assumed. As such, this
work should be useful to anyone interested in
category theory that finds programming to be a useful
tool in understanding abstract ideas. In addition,
as an introductory work, this book should prepare the
reader for more advanced literature in the field.