1990/09/01 by Colin McLarty · 1 citation
Arts and Humanities · Computer Science · Mathematics · #History and Theory of Mathematics #Philosophy and History of Science #Topological and Geometric Data Analysis
paper · doi:10.1093/bjps/41.3.351
openalex publication_date 1990/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
The view that toposes originated as generalized set theory is a figment of set theoretically educated common sense. This false history obstructs understanding of category theory and especially of categorical foundations for mathematics. Problems in geometry, topology, and related algebra led to categories and toposes. Elementary toposes arose when Lawvere's interest in the foundations of physics and Tierney's in the foundations of topology led both to study Grothendieck's foundations for algebraic geometry. I end with remarks on a categorical view of the history of set theory, including a false history plausible from that point of view that would make it helpful to introduce toposes as a generalization from set theory.