DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17

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.

Co-Eilenberg–Moore category of a comonad

Definition

For a comonad $G$ on $C$ , the co-Eilenberg–Moore category $C_{G}$ has $G$ -coalgebras as objects and coalgebra homomorphisms as morphisms. Its identities and composition are those of $C$ , whose closure is supplied by Coalgebra homomorphisms are closed under identities and composition. The forgetful functor $U^{G} : C_{G} \to C$ sends a coalgebra and a coalgebra homomorphism to their underlying object and arrow.

Depends on

Coalgebra homomorphisms are closed under identities and composition

Used by

The cofree–forgetful co-Eilenberg–Moore adjunction induces the given comonad Theorem

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 3 results over 3 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

E. Riehl, Category Theory in Context, 2nd ed., Exercise 5.2.iii (standard reference, not scraped)