leanprover-community/mathlib4
Strict group homs are stable by `Prod.map`
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#38 421 ouverte le 23 avr. 2026
enhancementgood first issuet-topology
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Description
Mathlib now has the definition Topology.IsStrictMap of topologically strict maps. In general, the product (in the sense of Prod.map) of two strict maps need not be strict. However, strict group homomorphisms satisfy this property.
I don't think we need a definition of strictness specific to group homs, but we definitely need some API :
- we should restate the definitions and characterizations in terms of MonoidHom.rangeRestrict, QuotientGroup.kerLift, and QuotientGroup.quotientKerEquivRange
- thanks to MonoidHom.isOpenQuotientMap_of_isQuotientMap, we can replace
IsQuotientMapbyIsOpenQuotientMapin this setting - then, the result should follow from IsOpenQuotientMap.prodMap (which is false for general quotient maps) and Homeomorph.Set.prod (and maybe an extra lemma saying that strict maps stay strict when we compose them with homeomorphisms)