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[Merged by Bors] - feat(category_theory/category/{Pointed,Bipointed}): The categories of pointed/bipointed types #11777
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… pointed/bipointed types (#11777) Define * `Pointed`, the category of pointed types * `Bipointed`, the category of bipointed types * the forgetful functors from `Bipointed` to `Pointed` and from `Pointed` to `Type*` * `Type_to_Pointed`, the functor from `Type*` to `Pointed` induced by `option` * `Bipointed.swap_equiv` the equivalence between `Bipointed` and itself induced by `prod.swap` both ways.
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Define
Pointed, the category of pointed typesBipointed, the category of bipointed typesBipointedtoPointedand fromPointedtoType*Type_to_Pointed, the functor fromType*toPointedinduced byoptionBipointed.swap_equivthe equivalence betweenBipointedand itself induced byprod.swapboth ways.Next, I'll define the monoidal structure on
Bipointedgiven by the pointed sum.