English
From a set of subobjects of A, construct the wide cospan diagram with a small indexing type; this yields a diagram in C whose shape is a wide pullback shape.
Русский
Из множества подпредметов A строится диаграмма широкого косопана, индексируемая небольшим множеством; получается диаграмма в C с формой широкого распятия.
LaTeX
$$def wideCospan {A : C} (s : Set (Subobject A)) : WidePullbackShape (equivShrink _ '' s) ⥤ C$$
Lean4
/-- The "wide cospan" diagram, with a small indexing type, constructed from a set of subobjects.
(This is just the diagram of all the subobjects pasted together, but using `WellPowered C`
to make the diagram small.)
-/
def wideCospan {A : C} (s : Set (Subobject A)) : WidePullbackShape (equivShrink _ '' s) ⥤ C :=
WidePullbackShape.wideCospan A (fun j : equivShrink _ '' s => ((equivShrink (Subobject A)).symm j : C)) fun j =>
((equivShrink (Subobject A)).symm j).arrow
