Abstract & Pure

Learn Homological Algebra

The computational technology below the first course and the derived-category tier above it: minimal free resolutions, Hochster's formula, triangulated categories, and what a resolution becomes once quasi-isomorphisms are inverted.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Homological Algebra

Diagram lemmas beyond the snakeInjective objects and injective hullsThe horseshoe lemma and comparisonThe Koszul complexMinimal free resolutionsHochster's formulaThe universal coefficient theoremCartan-Eilenberg resolutionsThe homotopy category of complexesTriangulated categoriesThe derived categoryVerdier localisationRHom and the derived tensor productt-structures and heartsThe Dold-Kan correspondenceSimplicial resolutionsHochschild homologyQuivers and Auslander-Reiten theory
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Homological Algebra exactly where it's useful.

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