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<p>We study the symmetric monoidal 2-category of finite semisimple module categories over a symmetric fusion category. In particular, we study <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_412_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(E_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>-algebras in this 2-category and compute their <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_412_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(E_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>-centers for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_412_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(n=0,1,2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. We also compute the factorization homology of stratified surfaces with coefficients given by <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_412_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(E_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>-algebras in this 2-category for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_412_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(n=0,1,2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> satisfying certain anomaly-free conditions.</p>

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Algebras Over a Symmetric Fusion Category and Integrations

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Xiao-Xue Wei

摘要

We study the symmetric monoidal 2-category of finite semisimple module categories over a symmetric fusion category. In particular, we study \(E_n\) E n -algebras in this 2-category and compute their \(E_n\) E n -centers for \(n=0,1,2\) n = 0 , 1 , 2 . We also compute the factorization homology of stratified surfaces with coefficients given by \(E_n\) E n -algebras in this 2-category for \(n=0,1,2\) n = 0 , 1 , 2 satisfying certain anomaly-free conditions.