Metric spaces, generalized logic, and closed categories - Milan Journal of Mathematics
- ️Lawvere, F. William
- ️Sat Dec 01 1973
Sunto
In questo articolo viene rigorosamente sviluppata l'analogia fra dist (a, b)+dist (b, c)≥dist (a, c) e hom (A, B) ⊗ hom (B, C)→ hom (A, C), giungendo a numerosi risultati generali sugli spazi metrici, come conseguenza di una «logica pura generalizzata» i cui «valori di verità» sono scelti in una arbitraria categoria chiusa.
Summary
The analogy between dist (a, b)+dist (b, c)≥dist (a, c) and hom (A, B) ⊗ hom (B, C)→hom (A, C) is rigorously developed to display many general results about metric spaces as consequences of a «generalized pure logic» whose «truth-values» are taken in an arbitrary closed category.
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Reference
MacLane S.,Categories for the Working Mathematician Springer 1972.
Eilenberg S. & Kelly G. M.,Closed Categories, in Proceedings of La Jolla Conference on Categorical Algebra. Springer 1966.
Benabou Jean,Les Distributeurs, Raport no 33, janvier 1973, Seminaires de Mathématiques Pure, Institut de Mathématiques, Université Catholique de Louvain (multigraphed).
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dell' Università di Perugia, Perugia, Italia
F. William Lawvere
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- F. William Lawvere
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(Conferenza tenuta il 30 marzo 1973)
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Lawvere, F.W. Metric spaces, generalized logic, and closed categories. Seminario Mat. e. Fis. di Milano 43, 135–166 (1973). https://doi.org/10.1007/BF02924844
Received: 16 November 1973
Issue Date: December 1973
DOI: https://doi.org/10.1007/BF02924844