## Categories and Computer ScienceCategory theory has become increasingly important and popular in computer science, and many universities now have introductions to category theory as part of their courses for undergraduate computer scientists. The author is a respected category theorist and has based this textbook on a course given over the last few years at the University of Sydney. The theory is developed in a straightforward way, and is enriched with many examples from computer science. Thus this book meets the needs of undergradute computer scientists, and yet retains a level of mathematical correctness that will broaden its appeal to include students of mathematics new to category theory. |

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algebra alphabet arrow f arrows 1x associative law axioms behaviour bijection called cartesian closed categories category theory category with products circuit codomain components composition table computer science confluent construct context-free data type defined Definition denote directed graphs distributive category distributive law elements empty end object equations Example false flow chart following diagram commutes free category free monoid function f functional specification functor F given functions graph morphism Hence identity arrows imperative program initial input IR+IR IRē isomorphism left Kan extension multigraph natural numbers natural transformation nodes null symbols operations pair of objects paths preorder queue real numbers regular grammar regular language relations satisfying sets and functions Show space stack Stack(X subpath subsets sums Suppose terminal object test(x Turing machine u₁ unique arrow universal property Walters R. F. C. Y₁ ᏞᏰ