DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge 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.

Weakly initial object and jointly weakly initial set

Definition

An object $W$ of a category $C$ is weakly initial if, for every object $C$ , there exists at least one morphism $W \to C$ . Unlike an initial object (Initial object, terminal object, and zero object), a weakly initial object need not have a unique morphism to each target.

A supplied set $S$ of objects is jointly weakly initial if, for every object $C$ , there exist $S \in S$ and a morphism $S \to C$ . The word supplied means that the set $S$ is part of the data; it does not mean that a witness is simultaneously chosen for every target.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 10 results over 6 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

T. Leinster, Basic Category Theory, Appendix A (standard reference, not scraped)