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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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Category theory, applications to the foundations of mathematics
2018Since the 1960s Lawvere has distinguished two senses of the foundations of mathematics. Logical foundations use formal axioms to organize the subject. The other sense aims to survey ‘what is universal in mathematics’. The ontology of mathematics is a third, related issue.
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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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On graph theoretical SAR and the mathematical theory of categories
Journal of Molecular Structure: THEOCHEM, 1991Abstract Chemical graph theory provides a special framework for solving many structure-activity relationship (SAR) problems such as boiling points, resonance energies, and pharmacological properties. The theorems by Muirhead (1901) and Karamata (1932), whereby certain sequences of numbers may be compared, have been used to establish SARs.
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Category Theory and the Foundations of Mathematics
The British Journal for the Philosophy of Science, 1981openaire +1 more source
Category theory and foundations of life science: A structuralist perspective on cognition
BioSystems, 2021Yoshihiro Maruyama
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