Theorems · Theorem · Lie groups
MonoidHom.isStrictMap_iff_isEmbedding_kerLift
∀ {G : Type u_1} {H : Type u_2} [inst : Group G] [inst_1 : Group H] {f : G →* H} [inst_2 : TopologicalSpace G]
[inst_3 : TopologicalSpace H], Topology.IsStrictMap ⇑f ↔ Topology.IsEmbedding ⇑(QuotientGroup.kerLift f)A group homomorphism is strict if and only if its QuotientGroup.kerLift is an embedding.
- Defined in
- Mathlib.Topology.Maps.Strict.Group
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Topology.IsEmbeddingstatement · cited by 294
- MonoidHom.kerstatement and proof · cited by 212
- Topology.IsStrictMapstatement and proof · cited by 45
- QuotientGroup.kerLiftstatement and proof · cited by 8
- Topology.IsQuotientMap.isStrictMap_iffproof · cited by 8
- QuotientGroup.isQuotientMap_mkproof · cited by 3
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