Theorems · Theorem · group theory
Rep.res_map_exact
∀ {G : Type v1} {H : Type v2} [inst : Monoid G] [inst_1 : Monoid H] (f : H →* G) {k : Type u} [inst_2 : CommRing k]
(S : CategoryTheory.ShortComplex (Rep.{w, u, v1} k G)), (S.map (Rep.resFunctor f)).Exact ↔ S.ExactThe instances above show that the restriction functor res φ : Rep R G ⥤ Rep R H
preserves and reflects exactness.
- Defined in
- Mathlib.RepresentationTheory.Rep.Res
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement and proof · cited by 3,629
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- Repstatement and proof · cited by 843
- CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292
- CategoryTheory.ShortComplex.mapstatement · cited by 188
- Rep.resFunctorstatement and proof · cited by 29
- CategoryTheory.ShortComplex.exact_map_iff_of_faithfulproof · cited by 3
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