Documentation

Atlas.AlgebraicTopologyI.code.CupProductHelpers

Categorical exactness of the kernel inclusion in ModuleCat (Section 28 helper for the cup product). For any morphism f : A ⟶ B in ModuleCat R, the underlying linear-map sequence kernel.ι f → f is exact in the sense of Function.Exact: the image of kernel.ι f coincides with the kernel of f. This bridges Mathlib's categorical kernel.ι with the concrete linear-algebra notion of exactness used in the cohomology development.