Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Supplied projective resolution data
Definition
Let be an abelian category, and let be a class of objects of .
A supplied projective resolution datum on assigns to each a specific projective resolution in the sense of Projective resolutions in an abelian category.
This is extra structure on the chosen domain of objects. It records displayed resolutions objectwise; it does not assert that such a choice exists canonically for all objects of .
Depends on
Used by
- Left derived objects relative to supplied projective resolution data Definition
- FALSE: enough projectives imply a canonical resolution for every object False statement
- A morphism has a comparison lift between the supplied projective resolutions Lemma
- Objectwise comparison of two projective resolution data induces an isomorphism on derived objects Lemma
Dependency tree · two levels
7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Charles A. Weibel, An Introduction to Homological Algebra, Chapter 2 `Derived Functors` (standard reference, not scraped)