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F. William Lawvere [3]F. W. Lawvere [1]
  1. F. William Lawvere (2003). Foundations and Applications: Axiomatization and Education. Bulletin of Symbolic Logic 9 (2):213-224.
    Foundations and Applications depend ultimately for their existence on each other. The main links between them are education and the axiomatic method. Those links can be strengthened with the help of a categorical method which was concentrated forty years ago by Cartier, Grothendieck, Isbell, Kan, and Yoneda. I extended that method to extract some essential features of the category of categories in 1965, and I apply it here in section 3 to sketch a similar foundation within the smooth categories which (...)
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  2. F. W. Lawvere (1994). Cohesive Toposes and Cantor's 'Lauter Einsen'. Philosophia Mathematica 2 (1):5-15.
    For 20th century mathematicians, the role of Cantor's sets has been that of the ideally featureless canvases on which all needed algebraic and geometrical structures can be painted. (Certain passages in Cantor's writings refer to this role.) Clearly, the resulting contradication, 'the points of such sets are distinc yet indistinguishable', should not lead to inconsistency. Indeed, the productive nature of this dialectic is made explicit by a method fruitful in other parts of mathematics (see 'Adjointness in Foundations', Dialectia 1969). This (...)
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  3. F. William Lawvere (1992). Categories of Space and of Quantity. In Javier Echeverria, Andoni Ibarra & Thomas Mormann (eds.), The Space of Mathematics. De Gruyter. 14--30.
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  4. F. William Lawvere (1969). Adjointness in Foundations. Dialectica 23 (3‐4):281-296.
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