[Merged by Bors] - refactor(Algebra/Homology): remove single₀#8208
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[Merged by Bors] - refactor(Algebra/Homology): remove single₀#8208
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This PR removes the special definitions of `single₀` for chain and cochain complexes, so as to avoid duplication of code with `HomologicalComplex.single` which is the functor constructing the complex that is supported by a single arbitrary degree. `single₀` was supposed to have better definitional properties, but it turns out that in Lean4, it is no longer true (at least for the action of this functor on objects). The computation of the homology of these single complexes is generalized for `HomologicalComplex.single` using the new homology API: this result is moved to a separate file `Algebra.Homology.SingleHomology`.
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This PR removes the special definitions of `single₀` for chain and cochain complexes, so as to avoid duplication of code with `HomologicalComplex.single` which is the functor constructing the complex that is supported by a single arbitrary degree. `single₀` was supposed to have better definitional properties, but it turns out that in Lean4, it is no longer true (at least for the action of this functor on objects). The computation of the homology of these single complexes is generalized for `HomologicalComplex.single` using the new homology API: this result is moved to a separate file `Algebra.Homology.SingleHomology`.
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This PR removes the special definitions of
single₀for chain and cochain complexes, so as to avoid duplication of code withHomologicalComplex.singlewhich is the functor constructing the complex that is supported by a single arbitrary degree.single₀was supposed to have better definitional properties, but it turns out that in Lean4, it is no longer true (at least for the action of this functor on objects). The computation of the homology of these single complexes is generalized forHomologicalComplex.singleusing the new homology API: this result is moved to a separate fileAlgebra.Homology.SingleHomology.After this, the plan is to refactor
CategoryTheory.Abelian.RightDerivedso as to use the new homology API.