DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-28

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.

Image and coimage in a category with kernels and cokernels

The image of $f$ is the kernel of a cokernel of $f$ :

$im (f) : = \ker (coker (f)) .$

The coimage of $f$ is the cokernel of a kernel of $f$ :

$coim (f) : = coker (\ker (f)) .$

This page uses the object notation $im (f)$ and $coim (f)$ . Their defining arrows are the corresponding kernel and cokernel maps.

Depends on