Marquis J.P. — Logic, epistemology, and the unity of science (№16 2009). From a Geometrical point of view. A study of the history and philosophy of category theory

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Название: Logic, epistemology, and the unity of science (№16 2009). From a Geometrical point of view. A study of the history and philosophy of category theory

Автор: Marquis J.P.

Аннотация:

Category theory is now pari and parcel of contemporary mathematics, theoretical computer science and even mathematical physics. And it is here to stay, for good reasons. However, these reasons are not clear to everyone, even within the mathematical community. Category theory is hard to learn and master. It is abstract. It is general. Someone has even said that it is "general abstract nonsense" (but it was meant as a joke). What is the point? Why bother? The point is that not only is it mathematically rich, deep and profound, but it is more generally conceptually rich, deep and profound. What does it take to see this? Understanding a specific important case is a place lo start.
Nowadays, no one would deny the importance of group theory in mathematics, physics, chemistry and science in general. Groups show up everywhere and whenever they do. their presence is significant, useful, and reveals deep and essential conceptual components of a situation. But it took almost a century for the community of scientists lo recognize this fact. According to many, groups were considered too abstract, too conceptual. The latter reaction might reveal more about those who pronounced it than about the field itself. The fact is: groups capture basic structural facts of a situation and allow for computations of otherwise intractable properties. It turns out. although this certainly was not intended to be an important part of the definition of a category, that groups are special cases of categories. It might take a century for the scientific community to recognize the importance of category theory. Indeed, it even took some time for category theorists themselves to recognize that categories, their properties and structures were as significant as groups, their properties and structures.