Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-05
How 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.

The trivial delta functor of an exact functor

Example

Assume the Axiom of Dependent Choice.

If A and B are abelian categories and F:A→B is exact, then the delta functor concentrated in degree 0, T0=F,Tn=0 for n>0, with zero connecting maps, is a universal homological delta functor; likewise the cohomological family T0=F,Tn=0 for n>0 with zero connecting maps is universal.

Facts & Assumptions

Given: An exact functor F between abelian categories.

[L1]

An exact base functor has precisely these trivial universal delta functors (An exact base functor has the trivial universal delta functor).

Verification

technique · direct
1.1L1given

The displayed homological and cohomological families are exactly the two families identified in [L1].

2.1L1step 1.1∎

Therefore both are universal delta functors.

Depends on

Used by

Nothing in the library uses this result yet.

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