Foundations

Learn Category theory (intro)

Math at its highest level of abstraction, all about structure-preserving maps.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

40 lessons in Category theory (intro)

CategoriesFunctorsNatural transformationsProducts & coproductsAdjoint functorsMonadsLimits & colimitsYoneda lemma (full)Abelian categoriesKan extensionsTopos theory introSheaves & presheavesHigher categoriesModel categoriesProof: limits are unique up to unique isoProof outline: Yoneda lemmaProof: adjoints preserve limits/colimitsOperadsMonoidal categoriesDuality & the opposite categoryRepresentable functorsUniversal propertiesEquivalence of categoriesThe category of elementsComma categoriesAlgebras for a monadCartesian closed categoriesEnds, coends & the coend calculusEnriched categoriesFibrations & the Grothendieck constructionThe adjoint functor theoremTopoi & the subobject classifierHomological algebra & derived functorsBeck's monadicity theoremSimplicial sets & the nerveChain complexes & homologyExact sequences & the snake lemmaDerived functors: Ext & TorGroup cohomologySpectral sequences
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 day its model predicts you would forget it. A short placement check finds what you already know, so you start Category theory (intro) exactly where it's useful.

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