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Published in:
2016 | OriginalPaper | Chapter
7. Basic Categorical Concepts
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Abstract
We have encountered, among others, the classes S (functions between sets), C (continuous mappings between convergence spaces), V (linear mappings between vector spaces), and CV. Members of these classes are triples of the form (domain, graph, and codomain). We have also encountered other classes of triples, e.g., the triples (x, ≤ , y) that arise in an up-directed set. The concept of category recognizes and exploits certain common features of such classes of triples of sets. For the sake of common generalization it introduces neutral terminology: the term “object” to represent “set” or “space” among possible choices; the term “arrow” or “morphism” to represent “function, mapping, homomorphism or relation” among possible choices.