DefinitionDefinition: AI-adaptedProof: Not applicablejudge 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-Kleisli category of a comonad

Definition

For a comonad $(G, ε, δ)$ on $C$ , the co-Kleisli category $C_{G}^{c o K l}$ has the objects of $C$ and hom-collections

$C_{G}^{c o K l} (A, B) = C (G A, B) .$

Composition is $g ⋆ f = g G (f) δ_{A}$ , and the identity of $A$ is $ε_{A}$ . These operations form a category by Co-Kleisli composition is associative and unital.

Depends on

Co-Kleisli composition is associative and unital

Used by

The co-Kleisli adjunction induces the given comonad Theorem

Dependency tree · two levels

3 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

E. Riehl, Category Theory in Context, 2nd ed., Definition 5.2.10 by formal duality (standard reference, not scraped)