Category Theory and Mathematical Structuralism

?

Category Theory and Mathematical Structuralism

P. 37–40.

Родин А. В.

Category theory doesn't support Mathematical Structuralism but suggests a new philosophical view on
mathematics, which differs both from Structuralism and from traditional Substantialism about mathematical
objects. While Structuralism implies thinking of mathematical objects up to isomorphism the new categorical
view implies thinking up to general morphism.

Язык: английский

Ключевые слова: Mathematical Structuralism

В книге

XXII World Congress of Philosophy

Vol. 41: Philosophy of mathematics. , [б.и.], 2008.

Categories Without Structures

Родин А. В., Philosophia Mathematica 2011 Vol. 19 No. 1 P. 20–46

The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies invariant forms (Awodey) categorical mathematics studies covariant transformations which, generally, don t have any invariants. In this paper I develop a non-structuralist interpretation of categorical ...

Добавлено: 5 июня 2018 г.