Preservation of colimits through composition #
This file records preservation results that only concern functor composition. No adjunction is involved.
theorem
CategoryTheory.Limits.preservesColimit_comp_left
{C : Type u_1}
[Category.{u_6, u_1} C]
{D : Type u_2}
[Category.{u_7, u_2} D]
{E : Type u_3}
[Category.{u_8, u_3} E]
{L : Functor C D}
(F : Functor D E)
{K : Type u_4}
[Category.{u_5, u_4} K]
(d : Functor K C)
[HasColimit d]
[PreservesColimit d L]
[PreservesColimit d (L.comp F)]
:
PreservesColimit (d.comp L) F
If L and L ⋙ F both preserve the colimit of d, then F preserves the colimit of
d ⋙ L.