https://sguzman.github.io/marginalia/tags/homology/Recent content in Homology on MarginaliaHugoen-usThu, 12 Feb 2026 00:00:00 +0000https://sguzman.github.io/marginalia/posts/homological-algebra/Thu, 12 Feb 2026 00:00:00 +0000https://sguzman.github.io/marginalia/posts/homological-algebra/Homological algebra grew out of 19th-century topology and became a central 20th-century language for modern mathematics. This essay traces the field from early homology invariants (Riemann, Betti, Poincaré) through Noether’s structural viewpoint, the Eilenberg–Mac Lane categorical turn, the Cartan–Eilenberg synthesis of derived functors, and the Grothendieck/Verdier revolution of abelian and derived categories. It closes with late-20th and 21st century developments including dg- and infinity-categories, derived algebraic geometry, and ongoing computational practice.