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14 items with this tag.
Oct 19, 2026
THEORY-729: An adjunction between a category and the opposite of another restricts to a dual equivalence between the full subcategories on which its unit and counit are isomorphisms
mathematics
philosophy-of-mathematics
Oct 16, 2026
THEORY-401: A fair lottery on the natural numbers has a uniform, regular probability defined on every set of tickets, by normalised numerosity with values in the hyperrationals; it is fixed only up to a choice of free ultrafilter, it is hyperfinitely and not countably additive, and its standard part is ordinary asymptotic density
philosophy-of-mathematics
epistemology
mathematics
Oct 16, 2026
THEORY-604: Most mathematical dualities are adjunctions between one category and the opposite of another, which become dual equivalences on their fixed points; what makes them dualities rather than equivalences is the reversal of arrows, so many of the 'dualities' physicists name are, in the mathematician's sense, equivalences or symmetries
philosophy-of-mathematics
mathematics
philosophy-of-science
Oct 01, 2026
LIT-437: Gödel, Escher, Bach: an Eternal Golden Braid
cognition
consciousness
logic
philosophy-of-mathematics
individuation
self
Sep 30, 2026
THEORY-032: The Yoneda lemma determines an object only up to isomorphism, from its whole hom-functor, among objects the category already has; as a formal version of "an object is determined by its relations" it presupposes the relata
philosophy-of-mathematics
mathematics
individuation
metaphysics
Sep 30, 2026
THEORY-038: Category theory gives radical ontic structural realism no formal support: generalized elements exist in every category, morphisms relate objects the category presupposes, and Bain's physical cases eliminate spacetime points, not relata
philosophy-of-science
metaphysics
philosophy-of-mathematics
mathematics
Sep 26, 2026
LIT-104: Philosophy of Mathematics from Descartes to Kant
philosophy-of-mathematics
epistemology
metaphysics
Sep 26, 2026
LIT-108: Philosophy of Mathematics and Natural Science
philosophy-of-science
philosophy-of-mathematics
mathematics
natural-sciences
Sep 26, 2026
LIT-115: Duality as a category-theoretic concept
philosophy-of-mathematics
mathematics
philosophy-of-science
individuation
Sep 26, 2026
LIT-151: Stating Structural Realism: Mathematics-First Approaches to Physics and Metaphysics
philosophy-of-science
metaphysics
philosophy-of-mathematics
Sep 26, 2026
LIT-154: Criteria of Identity and Structuralist Ontology
individuation
philosophy-of-mathematics
mathematics
metaphysics
Sep 26, 2026
LIT-163: Philosophy of Probability: Foundations, Epistemology, and Computation
epistemology
philosophy-of-mathematics
probabilistic-modeling
philosophy-of-science
Sep 26, 2026
LIT-222: No categorial support for radical ontic structural realism
philosophy-of-science
metaphysics
philosophy-of-mathematics
Sep 26, 2026
LIT-223: Category-theoretic structure and radical ontic structural realism
philosophy-of-science
metaphysics
philosophy-of-mathematics