Categories for the working mathematician
Book
Foundational Source
Category Theory
Citation
Mac Lane, Saunders. (1971). Categories for the working mathematician. Springer.
Why this reference is included
Mac Lane’s Categories for the working mathematician (1971), published by Springer, sits in the program’s reference corpus as a standing technical source. Cited across Book VII (Categorical Metaphysics), Part 2, Chapter Relational Primacy: Relations Precede Relata; Book VII (Categorical Metaphysics), Part 7, Chapter Dignity as Meta-Ethical Foundation — the central framing is “The categorical sharpening is decisive: the Yoneda Lemma provides a theorem, not merely a philosophical stance, that relational position determines identity”.
Cited in
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Book VII — Categorical Metaphysics Part 2Chapter Relational Primacy: Relations Precede Relata
The categorical sharpening is decisive: the Yoneda Lemma provides a theorem, not merely a philosophical stance, that relational position determines identity
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Book VII — Categorical Metaphysics Part 7Chapter Dignity as Meta-Ethical Foundation
(i)–(iii): By standard results on reflective subcategories and Lawvere–Tierney topologies (Mac Lane and Moerdijk, Sheaves in Geometry and Logic)