smallCoproductDesc — Mathlib

English

The universal morphism out of the coproduct of a set of subobjects, after indexing by a small type, is defined by Sigma.desc of the underlying subobjects.

Русский

Универсальная морфизма из coproduct множества подпредметов, индексированного малым типом, задаётся через Sigma.desc над отображениями подпредметов.

LaTeX

$$def smallCoproductDesc {A : C} (s : Set (Subobject A)) :=\n Limits.Sigma.desc fun j : equivShrink _ '' s => ((equivShrink (Subobject A)).symm j).arrow$$

Lean4

/-- The universal morphism out of the coproduct of a set of subobjects,
after using `[WellPowered C]` to reindex by a small type.
-/
def smallCoproductDesc {A : C} (s : Set (Subobject A)) :=
  Limits.Sigma.desc fun j : equivShrink _ '' s => ((equivShrink (Subobject A)).symm j).arrow

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