Theorems · Theorem · category theory

Function.MulExact.iff_monoidHom_rangeRestrict

∀ {M : Type u_2} {N : Type u_4} {P : Type u_6} [inst : Group M] [inst_1 : Group N] [inst_2 : Group P] {f : M →* N}
  {g : N →* P}, Function.MulExact ⇑f ⇑g ↔ Function.MulExact ⇑f.range.subtype ⇑g.rangeRestrict

Two maps f : M →* N and g : N →* P are exact if and only if the induced maps MonoidHom.range f → N → MonoidHom.range g are exact.

Defined in

Mathlib.Algebra.Exact.Basic

Cited by

1 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupGroup