[Merged by Bors] - feat(Algebra/Homology): commutation up to signs of the compatibility isomorphisms of the total complex with shifts in both variables #11517
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…o homological-complex-mapbifunctor + more API
…' into homological-complex-mapbifunctor-homotopy
… on the first variable
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
…' into homological-complex-mapbifunctor-homotopy
…' into total-complex-shift
…' into cochain-complex-mapbifunctor-shift
…ft' into total-complex-shift-compatibility
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…isomorphisms of the total complex with shifts in both variables (#11517) Shifting horizontally a bicomplex by an integer `x` and then taking the total complex gives a cochain complex that is isomorphic to the shift of the total complex of the original bicomplex. The same applies to vertical shifts by an integer `y`. However, when we apply both horizontal and vertical shifts, depending on whether we apply the horizontal shift or the vertical shift first, we get two isomorphisms which differ by the sign `(x * y).negOnePow`. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…isomorphisms of the total complex with shifts in both variables (#11517) Shifting horizontally a bicomplex by an integer `x` and then taking the total complex gives a cochain complex that is isomorphic to the shift of the total complex of the original bicomplex. The same applies to vertical shifts by an integer `y`. However, when we apply both horizontal and vertical shifts, depending on whether we apply the horizontal shift or the vertical shift first, we get two isomorphisms which differ by the sign `(x * y).negOnePow`. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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Shifting horizontally a bicomplex by an integer
xand then taking the total complex gives a cochain complex that is isomorphic to the shift of the total complex of the original bicomplex. The same applies to vertical shifts by an integery. However, when we apply both horizontal and vertical shifts, depending on whether we apply the horizontal shift or the vertical shift first, we get two isomorphisms which differ by the sign(x * y).negOnePow.