homological algebra

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• kernel -- kernel of a map
• cokernel -- cokernel of a map
• image -- image of a map
• coimage -- coimage of a map
• preimage -- preimage of a map
• pullback -- compute the pullback morphism
• pushout -- compute the pushout morphism
• extend -- extend an object
• nullhomotopy -- make a null homotopy
• isExact
• isInjective -- whether a map is injective
• isSurjective -- whether a map is surjective
• isIsomorphism -- whether a map is an isomorphism
• inverse -- compute the inverse
• ScriptedFunctor -- the class of all scripted functors
• id -- identity map
• HH -- general homology and cohomology functor
• Tor -- Tor module
• Ext -- compute an Ext module