algebra / Tensor categories

Does every abelian envelope have the quotient property?

No. The universal rigid monoidal category on one object has an abelian envelope, which by the 2023 no-go result cannot have the quotient property.

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No. The universal rigid monoidal category on one object has an abelian envelope, which by the 2023 no-go result cannot have the quotient property.

No. The universal rigid monoidal category on one object has an abelian envelope, which by the 2023 no-go result cannot have the quotient property.

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Does every abelian envelope have the quotient property? — Mathematical Frontier Network