Diagrams as sketches |
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Authors: | Brice Halimi |
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Institution: | 1. D??partement de Philosophie (IREPH), Universit?? Paris Ouest, Nanterre, France 2. SPHERE (UMR 7219), Universit?? Paris-Diderot, Paris, France
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Abstract: | This article puts forward the notion of ??evolving diagram?? as an important case of mathematical diagram. An evolving diagram combines, through a dynamic graphical enrichment, the representation of an object and the representation of a piece of reasoning based on the representation of that object. Evolving diagrams can be illustrated in particular with category-theoretic diagrams (hereafter ??diagrams*??) in the context of ??sketch theory,?? a branch of modern category theory. It is argued that sketch theory provides a diagrammatic* theory of diagrams*, that it helps to overcome the rivalry between set theory and category theory as a general semantical framework, and that it suggests a more flexible understanding of the opposition between formal proofs and diagrammatic reasoning. Thus, the aim of the paper is twofold. First, it claims that diagrams* provide a clear example of evolving diagrams, and shed light on them as a general phenomenon. Second, in return, it uses sketches, understood as evolving diagrams, to show how diagrams* in general should be re-evaluated positively. |
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