In this talk, we will examine standard built-in functions of computer programming, such as unique, ismember, sortrows, sparse, and others, by extracting their categorical properties. We will introduce a procedure to implement a programming function called coeq, which exhibits categorical behavior similar to a coequalizer. As an application, we will consider the problem of transforming an arbitrary graph, encoded in MATLAB and Octave, as a pair of complex-valued matrices of equal size (dom, cod), into a triplet (s, t, v), satisfying dom = v(s) and cod = t(v). Additionally, we will present some ideas on defining a category of structured sets as a preliminary step towards establishing a mathematical foundation for computer science, which combines the fundamental concept of a set with a specific structure for storing its elements as a list within a computer.
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