Corpus definition canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Definition cid001319DEF0193canonicalv1

Homology via SES

Homology via short exact sequences: 0 → Z/M_{k-1} → Z/M_k → Z/p_k → 0. Exactness at the middle: ker(g) = im(f), giving trivial homology H = 0.

Payload

Homology via SES

Homology via short exact sequences: 0 → Z/M_{k-1} → Z/M_k → Z/p_k → 0. Exactness at the middle: ker(g) = im(f), giving trivial homology H = 0.

Homology via SES

Summary

Homology via short exact sequences: 0 → Z/M_{k-1} → Z/M_k → Z/p_k → 0. Exactness at the middle: ker(g) = im(f), giving trivial homology H = 0.

Statement

No manuscript statement was extracted in this pilot run.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

  • Registry source: book-02.jsonl line 209
  • Manuscript source: not matched

Lean / Formalization Notes

  • Formalization: formalized
  • Module: TauLib.BookII.Enrichment.Homological
  • Name: ses_exactness_check

Dependencies

  • Canonical: II.D84

Generated by later projection phases.

Generated by later projection phases.

Revision Notes

  • 2026-04-24: Initial pilot migration.

Identifiers

  • Corpus ID cid001319
  • Primary alias DEF0193
  • Type Definition
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

II.D85homology-via-sesdef:homology-ses

Release lines

corpus_v3_workingcorpus_v2

Relations

Formalized by (4)

cid005502cid005503cid005504cid005505

Appears in (1)

cid000001

Downstream uses (computed) (8)

Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.

FTH0240formal theorem FTH0240formal theorem FTH0241formal theorem FTH0241formal theorem FTH0242formal theorem FTH0242formal theorem FTH0243formal theorem FTH0243formal theorem

Sources

  • Monograph cid000001Book II, Part 8, Chapter 46 (Wave M5)

Version & History

  • v1 · 2026-05-10 imported from v2 registry
  • v1 · 2026-05-10 wired formalized by in wave 5

Status disclaimer

A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.

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