[Merged by Bors] - feat(Algebra/Homology): the action of a bifunctor on homological complexes factors through homotopies #10800
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…o homological-complex-mapbifunctor + more API
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…lexes factors through homotopies (#10800) Given a `TotalComplexShape c₁ c₂ c`, a functor `F : C₁ ⥤ C₂ ⥤ D`, we study the behavior with respect to homotopies or the functoriality of the action of `F` on homological complexes: if `f₁` and `f₁'` are homotopic maps, then the maps `mapBifunctorMap f₁ f₂ F c` and `mapBifunctorMap f₁' f₂ F c` are also homotopic. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…lexes factors through homotopies (#10800) Given a `TotalComplexShape c₁ c₂ c`, a functor `F : C₁ ⥤ C₂ ⥤ D`, we study the behavior with respect to homotopies or the functoriality of the action of `F` on homological complexes: if `f₁` and `f₁'` are homotopic maps, then the maps `mapBifunctorMap f₁ f₂ F c` and `mapBifunctorMap f₁' f₂ F c` are also homotopic. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…lexes factors through homotopies (#10800) Given a `TotalComplexShape c₁ c₂ c`, a functor `F : C₁ ⥤ C₂ ⥤ D`, we study the behavior with respect to homotopies or the functoriality of the action of `F` on homological complexes: if `f₁` and `f₁'` are homotopic maps, then the maps `mapBifunctorMap f₁ f₂ F c` and `mapBifunctorMap f₁' f₂ F c` are also homotopic. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…lexes factors through homotopies (#10800) Given a `TotalComplexShape c₁ c₂ c`, a functor `F : C₁ ⥤ C₂ ⥤ D`, we study the behavior with respect to homotopies or the functoriality of the action of `F` on homological complexes: if `f₁` and `f₁'` are homotopic maps, then the maps `mapBifunctorMap f₁ f₂ F c` and `mapBifunctorMap f₁' f₂ F c` are also homotopic. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…lexes factors through homotopies (#10800) Given a `TotalComplexShape c₁ c₂ c`, a functor `F : C₁ ⥤ C₂ ⥤ D`, we study the behavior with respect to homotopies or the functoriality of the action of `F` on homological complexes: if `f₁` and `f₁'` are homotopic maps, then the maps `mapBifunctorMap f₁ f₂ F c` and `mapBifunctorMap f₁' f₂ F c` are also homotopic. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…lexes factors through homotopies (#10800) Given a `TotalComplexShape c₁ c₂ c`, a functor `F : C₁ ⥤ C₂ ⥤ D`, we study the behavior with respect to homotopies or the functoriality of the action of `F` on homological complexes: if `f₁` and `f₁'` are homotopic maps, then the maps `mapBifunctorMap f₁ f₂ F c` and `mapBifunctorMap f₁' f₂ F c` are also homotopic. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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Given a
TotalComplexShape c₁ c₂ c, a functorF : C₁ ⥤ C₂ ⥤ D, we study the behavior with respect to homotopies or the functoriality of the action ofFon homological complexes: iff₁andf₁'are homotopic maps, then the mapsmapBifunctorMap f₁ f₂ F candmapBifunctorMap f₁' f₂ F care also homotopic.Hopefully, it might be possible to deduce the symmetric property for the second variable from this result on the first variable and a study of the flip of functors...