coneMorphism_π — Mathlib

English

Let hc be an IsLimit hc cone for F, then the inverse of the conePointUniqueUpToIso composed with limit.π F j equals c.π.app j; this is the inverse-companion form of the universal property.

Русский

Пусть hc — IsLimit конус для F; тогда inv ∘ conePointUniqueUpToIso ≈ π_j даёт c.π.app j.

LaTeX

$$$(\\mathrm{IsLimit}.conePointUniqueUpToIso (\\mathrm{limit}.isLimit _) hc).inv \\;\\circ\\; \\mathrm{limit}.π F j = c.π.app j$$$

Lean4

theorem coneMorphism_π {F : J ⥤ C} [HasLimit F] (c : Cone F) (j : J) :
    (limit.coneMorphism c).hom ≫ limit.π F j = c.π.app j := by simp

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