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Explore the philosophical foundations of mathematical structuralism through a categorical lens in this comprehensive seminar lecture. Examine the criteria for mathematical structuralism as presented by Hellman and Shapiro in their 2019 publication, and analyze how category theory measures against these established standards. Delve into an alternative narrative that challenges conventional perspectives and leads to different conclusions about the nature of mathematical structures. Engage with a critical reevaluation of the criteria used to define mathematical structuralism, gaining insights into how categorical approaches can reshape our understanding of mathematical foundations. This presentation is part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics, offering a rigorous examination of contemporary debates in mathematical philosophy and the role of category theory in structural mathematics.
