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Category Theory: The Language of Mathematics
Philosophy of Science, 1999In this paper I argue that category theory ought to be seen as providing thelanguagefor mathematical discourse. Against foundational approaches, I argue that there is no need toreduceeither the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories.
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Mathematical Applications of Category Theory
1984The interaction between category theory and set theory by A. Blass Synthetic calculus of variations by M. Bunge and M. Heggie The representation of limits, lax limits and homotopy limits as sections by J. W. Gray Open locales and exponentiation by P. T. Johnstone Eilenberg-Mac Lane toposes and cohomology by A. Joyal and G. Wraith A combinatorial theory
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Semantic Category theory and Semantic Intertwine: the anathema of mathematics
Kybernetes, 2014Purpose – The recent scientific observation that human information processing involves four independent data types, has pinpointed a source of fallacious arguments within many domains of human thought. The species-unique ability to assign observable characteristics to purely conceptual entities has created beautiful ...
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Does Category Theory Provide a Framework for Mathematical Structuralism?†
Philosophia Mathematica, 2003Category theory and topos theory were suggested as a structuralist framework for mathematics autonomous w.r.t. set theory. The paper criticises this approach. It is argued that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves.
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Introduction to gestural similarity in music. An application of category theory to the orchestra
Journal of Mathematics and Music, 2018Maria Mannone
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