Technical Lean evidence record

Checked Artifact: Freyd–Mitchell Embedding Theorem (mathlib)

Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.

ProofAtlas record

What has been checked

Upstream indexedPinned source bytes verified locally

Locally reproducedExact upstream declaration replayed

Reviewed pageCurrent public presentation reviewed

Accepted Atlas resultNot recorded for the preferred artifact

These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.

Mechanical evidence

Declaration checked: CategoryTheory.Abelian.freyd_mitchell
Module: Mathlib.CategoryTheory.Abelian.FreydMitchell
Source file checked: Mathlib/CategoryTheory/Abelian/FreydMitchell.lean
Package commit: 5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build: passed · transcript retained
Unfinished proof steps: None found by the recorded no-sorry scan
Axiom closure: Classical.choice, Quot.sound, propext
Clean collection provenance: Recorded

Evidence boundary

This target indexes Mathlib's existential Freyd–Mitchell endpoint for a category C equipped with an Abelian instance: there exist a ring R and a functor F : C ⥤ ModuleCat R that is full, faithful, preserves finite limits, and preserves finite colimits. The universe of R and the module category is max u v. The statement is an embedding into a module category, not an equivalence onto that whole category.

This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.