preservesMonomorphisms_comp — Mathlib

English

The composition of two functors preserves monomorphisms if each preserves monomorphisms.

Русский

Сложение двух функторов сохраняет моно-морфизм, если каждый сохраняет моно.

LaTeX

$$[F PreservesMonomorphisms] ∧ [G PreservesMonomorphisms] ⇒ [(F ⋙ G).PreservesMonomorphisms]$$

Lean4

instance preservesMonomorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesMonomorphisms F] [PreservesMonomorphisms G] :
    PreservesMonomorphisms (F ⋙ G) where
  preserves f
    h := by
    rw [comp_map]
    exact inferInstance

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