Structure in mathematics and logic: A categorical perspective

Philosophia Mathematica 4 (3):209-237 (1996)
Abstract
A precise notion of ‘mathematical structure’ other than that given by model theory may prove fruitful in the philosophy of mathematics. It is shown how the language and methods of category theory provide such a notion, having developed out of a structural approach in modern mathematical practice. As an example, it is then shown how the categorical notion of a topos provides a characterization of ‘logical structure’, and an alternative to the Pregean approach to logic which is continuous with the modern structural approach in mathematics
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DOI 10.1093/philmat/4.3.209
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Structuralism, Invariance, and Univalence.Steve Awodey - 2014 - Philosophia Mathematica 22 (1):nkt030.
Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - forthcoming - British Journal for the Philosophy of Science:axw006.
Category Theory as an Autonomous Foundation.Øystein Linnebo & Richard Pettigrew - 2011 - Philosophia Mathematica 19 (3):227-254.
Structuralism, Invariance, and Univalence†: Articles.Steve Awodey - 2014 - Philosophia Mathematica 22 (1):1-11.

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