feat/refactor: redefinition of homology + derived categories#4197
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feat/refactor: redefinition of homology + derived categories#4197
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This PR has been migrated to a fork-based workflow: #25848 |
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This PR contains a redefinition of homology, theorems about localization of categories, including triangulated categories, a construction of the derived category of an abelian category, derived functors, spectral sequences, etc. (This is made a PR only to facilitate navigation in the code of this branch.)
This formalization is outlined in the paper Formalization of derived categories in Lean/mathlib https://hal.science/hal-04546712
The homology of
ShortComplex C(diagrams of two composable morphisms whose composition is zero) is developed inAlgebra.Homology.ShortComplex. The files in that folder have been added one by one in separate PRs, and then, the current definition ofhomologyhas been replaced by this new definition in a refactor PR.Homology refactor:
Homological complexes:
Localization of categories:
Shifts on categories:
Triangulated categories:
Construction of the derived category:
Derived functors:
Refactor of Ext-groups: