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<p>We give an elementary characterization of those quantaloids <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">Q</mi> </math></EquationSource> </InlineEquation> for which the category <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textsf{Cat}(\mathcal {Q})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="sans-serif">Cat</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">Q</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">Q</mi> </math></EquationSource> </InlineEquation>-enriched categories and functors is cartesian closed. We then unify several known cases (previously proven using <i>ad hoc</i> methods) and we give some new examples.</p>

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When is \(\textsf{Cat}(\mathcal {Q})\) Cartesian Closed?

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月1日

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  • Isar Stubbe,
  • Junche Yu

摘要

We give an elementary characterization of those quantaloids \(\mathcal {Q}\) Q for which the category \(\textsf{Cat}(\mathcal {Q})\) Cat ( Q ) of \(\mathcal {Q}\) Q -enriched categories and functors is cartesian closed. We then unify several known cases (previously proven using ad hoc methods) and we give some new examples.