category theory was invented in the tradition of Felix Klein’s Erlanger Programm, as a way of studying and characterizing different kinds of mathematical structures in terms of their “admissible trans- formations.” The general notion of a category provides a characterization of the notion of a “structure-preserving transformation,” and thereby of a species of structures admitting such transformations
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LustrzanyDotyk - (no access) - (Oxford Logic Guides 52) Steve Awodey-Category Theory-Oxford University Press (2010).pdf, p18
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