Semiseparability of induction functors in a monoidal category
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910010563362816 |
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| author | Bottegoni, Lucrezia Zuo, Zhenbang |
| author_facet | Bottegoni, Lucrezia Zuo, Zhenbang |
| contents | For any algebra morphism in a monoidal category, we provide sufficient conditions (which are also necessary if the unit is a left tensor generator) for the attached induction functor being semiseparable. Under mild assumptions, we prove that the semiseparability of the induction functor is preserved if one applies a lax monoidal functor. Similar results are shown for the coinduction functors attached to coalgebra morphisms in a monoidal category. As an application, we study the semiseparability of combinations of (co)induction functors in the context of duoidal categories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_03739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiseparability of induction functors in a monoidal category Bottegoni, Lucrezia Zuo, Zhenbang Category Theory Quantum Algebra Rings and Algebras Representation Theory Primary 18A22, Secondary 18M05, 18A40, 18M50 For any algebra morphism in a monoidal category, we provide sufficient conditions (which are also necessary if the unit is a left tensor generator) for the attached induction functor being semiseparable. Under mild assumptions, we prove that the semiseparability of the induction functor is preserved if one applies a lax monoidal functor. Similar results are shown for the coinduction functors attached to coalgebra morphisms in a monoidal category. As an application, we study the semiseparability of combinations of (co)induction functors in the context of duoidal categories. |
| title | Semiseparability of induction functors in a monoidal category |
| topic | Category Theory Quantum Algebra Rings and Algebras Representation Theory Primary 18A22, Secondary 18M05, 18A40, 18M50 |
| url | https://arxiv.org/abs/2602.03739 |