Alphabeta Math
RemarkRemark: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16
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.

Objectwise existence does not itself supply a class-sized choice of adjoint values

The reverse implications in A left adjoint exists exactly when chosen initial objects are supplied in every comma category and A supplied pointwise right adjoint extends uniquely to a functor begin with chosen objects as data. An assertion that a suitable object exists separately for every object of a proper class does not by itself provide one class-function selecting them all. This is the same distinction recorded for limit and colimit functors in A limit for each diagram need not provide a chosen limit functor without a simultaneous choice of representatives: after the object assignment is supplied, universal uniqueness determines the morphism assignment without further choice.

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Nothing in the library uses this result yet.

Dependency tree · two levels

12 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