Tag
Derived Functors
9 resources tagged “Derived Functors” across the knowledge library.
9 items
Guide6 Aug 2026Chain Complexes and HomologyChain and cochain complexes, cycles and boundaries, homology as a functor, and the abelian category of complexes.3 min readRead MoreGuide6 Aug 2026Chain Homotopy and the Comparison TheoremChain homotopy between chain maps, homotopy equivalence, the comparison theorem for projective resolutions, and independence of derived functors from the chosen resolution.4 min readRead MoreGuide6 Aug 2026Change of RingsRestriction and extension of scalars, induced and coinduced modules, the change-of-rings theorems, and the associated spectral sequences.3 min readRead MoreGuide6 Aug 2026Derived FunctorsLeft and right derived functors, their construction from resolutions, the fundamental properties, and the axiomatic characterisation by universality.4 min readRead MoreGuide6 Aug 2026Ext via Projective and Injective ResolutionsComputing Ext by resolving either variable, the double complex proof that the two agree, and the practical consequences for choosing a computation.4 min readRead MoreGuide6 Aug 2026Projective and Injective ResolutionsConstruction of projective and injective resolutions, the horseshoe lemma, projective and injective dimension, and global dimension of a ring.4 min readRead MoreGuide6 Aug 2026The Long Exact Homology SequenceThe long exact sequence associated to a short exact sequence of complexes, construction of the connecting homomorphism, naturality, and the standard applications.4 min readRead MoreGuide6 Aug 2026The Long Exact Sequences of Derived FunctorsDerivation of the long exact sequences of derived functors via the horseshoe lemma, their naturality, dimension shifting and the standard computational patterns.3 min readRead MoreGuide6 Aug 2026Yoneda Ext and n-Fold ExtensionsThe Yoneda description of Ext^n by n-fold extensions, the equivalence relation, splicing as composition, and the Yoneda product.4 min readRead More