Categories and Computer Science
Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.
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algebra alphabet arrows associative axioms beginning calculation called category with products Chapter circuit clear coincidences components composition computer science Consider consists constants construct contains corresponds defined Definition denote described distributive category elements empty equations exactly Example exists expression fact faithful functor false finite flow free category function f functor Further give given grammar graph Hence identity imperative program initial input isomorphism language length look machine mathematics monoid morphism multigraph multiply namely natural natural numbers natural transformation Note Notice objects obtained operations pair paths procedure projections push reductions regular language relations Remark satisfying Show space specified stack subsets sums Suppose symbol tables transfer trees true unique arrow universal property write