RemarkRemark: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-04

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.

What 'left' refers to in 'left dual'

Remark

In this library, following EGNO, a left dual $X^{\lor}$ of $X$ is named by the side on which $X^{\lor}$ appears in the evaluation map $X^{\lor} \otimes X \to 1$ . Some sources name duals by the side on which the original object is adjoint instead; that convention reverses the words "left" and "right" relative to this page.

Depends on

Left dual and right dual object

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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

Michael Muger, Tensor Categories: A Selective Guided Tour, Section 1.5 (standard reference, not scraped)
P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Remark 2.10.3 (standard reference, not scraped)