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from Part One - Building up to Categories
Published online by Cambridge University Press: 13 October 2022
An overview of what the point of category theory is, without formality, and an overview of the contents of the book. We will present category theory as “the mathematics of mathematics”, so first we explain what aspects of mathematics we are focusing on. We present mathematics as starting from abstraction, as a way of elucidating analogies between situations, finding connections between them, and unifying them. Category theory is then a rigorous framework for making analogies and finding connections between different parts of mathematics. It focuses on relationships between things, rather than on intrinsic characteristics, and uses those relationships to put objects in context rather than treat them in isolation. Once the framework has been set up, we have, among other things, a way to express more nuanced notions of “sameness”, and a way to characterize things by the role they play in that context. Category theory also works at many different levels, so we can zoom in and out and study details close up, or broad contexts with more of an overview.
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