English
The retracts of transfinite pushouts and coproducts lie below the left lifting property; equivalently, retracts funnel through llp/rlp bounds.
Русский
Обратные отображения трансфинитных толпушек и копроизводов находятся ниже левых свойств подъёма; эквивалентно, retracts проходят через пределы llp/rlp.
LaTeX
$$$$ (coproducts\: W).pushouts.transfiniteCompositionsOfShape J \text{ retracts } \le W.rlp.llp $$$$
Lean4
theorem retracts_transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp :
((coproducts.{w} W).pushouts.transfiniteCompositionsOfShape J).retracts ≤ W.rlp.llp :=
by
rw [le_llp_iff_le_rlp, rlp_retracts, ← le_llp_iff_le_rlp]
apply transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp
