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  1. Homotopy Type Theory and Structuralism.Teruji Thomas - 2014 - Dissertation, University of Oxford
    I explore the possibility of a structuralist interpretation of homotopy type theory (HoTT) as a foundation for mathematics. There are two main aspects to HoTT's structuralist credentials. First, it builds on categorical set theory (CST), of which the best-known variant is Lawvere's ETCS. I argue that CST has merit as a structuralist foundation, in that it ascribes only structural properties to typical mathematical objects. However, I also argue that this success depends on the adoption of a strict typing system which (...)
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  • Pasch's empiricism as methodological structuralism.Dirk Schlimm - 2020 - In Erich H. Reck & Georg Schiemer (eds.), The Pre-History of Mathematical Structuralism. Oxford: Oxford University Press. pp. 80-105.
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  • Invariants and Mathematical Structuralism.Georg Schiemer - 2014 - Philosophia Mathematica 22 (1):70-107.
    The paper outlines a novel version of mathematical structuralism related to invariants. The main objective here is twofold: first, to present a formal theory of structures based on the structuralist methodology underlying work with invariants. Second, to show that the resulting framework allows one to model several typical operations in modern mathematical practice: the comparison of invariants in terms of their distinctive power, the bundling of incomparable invariants to increase their collective strength, as well as a heuristic principle related to (...)
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