## 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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alphabet associative law axioms behaviour bijection binary tree called cartesian closed categories category theory category with products circuit codomain components composition table computer science confluent cons(a construct context-free corresponds data type defined Definition denote directed graphs distributive category distributive law empty end object equations Example finite number finite set flow chart following diagram commutes free category free monoid functional specification functor F given functions graph morphism Hence identity arrows imperative program initial input isomorphism left adjoint left Kan extension mathematics multigraph natural numbers natural transformation nodes Note null symbols operations pair of objects paths pointer preorder pseudofunction push queue real numbers regular grammar regular language relations satisfying sets and functions Show space Stack(X subpath subsets Suppose terminal object test(x transfer Turing machine unique arrow universal property Walters R. F. C. Xi x X2