English
The lift and the nat-iso satisfy: limit.lift F t ≫ (HasLimit.isoOfNatIso w).hom = limit.lift G ((Cones.postcompose w.hom).obj _).
Русский
Лифтинг и нат-изоморфизм удовлетворяют: limit.lift F t ≫ (HasLimit.isoOfNatIso w).hom = limit.lift G ((Cones.postcompose w.hom).obj _).
LaTeX
$$$\\operatorname{limit.lift} F t \\gg (\\operatorname{HasLimit.isoOfNatIso} w).hom = \\operatorname{limit.lift} G ((\\operatorname{Cones.postcompose} w.hom).obj _)$$$
Lean4
/-- -
If we have particular limit cones available for `E ⋙ F` and for `F`,
we obtain a formula for `limit.pre F E`.
-/
theorem pre_eq (s : LimitCone (E ⋙ F)) (t : LimitCone F) :
limit.pre F E = (limit.isoLimitCone t).hom ≫ s.isLimit.lift (t.cone.whisker E) ≫ (limit.isoLimitCone s).inv := by
cat_disch
