leanprover-community/mathlib4

Strict group homs are stable by `Prod.map`

Open

#38,421 opened on Apr 23, 2026

View on GitHub
 (8 comments) (0 reactions) (0 assignees)Lean (1,381 forks)github user discovery
enhancementgood first issuet-topology

Repository metrics

Stars
 (3,405 stars)
PR merge metrics
 (No merged PRs in 30d)

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 :

Contributor guide

Research direction
Restate definitions using MonoidHom.rangeRestrict and QuotientGroup.kerLift, then apply MonoidHom.isOpenQuotientMap of isQuotientMap to replace IsQuotientMap with IsOpenQuotientMap, finally use IsOpenQuotientMap.prodMap and compose with homeomorphisms to prove that Prod.map preserves strict group homs.
Tech stack
None
Domain
None
Issue type
Feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
Half day
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
Active
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
Clear
Prerequisites
Lean
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
70