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YCor
YCor
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Is the Centercenter of an Abelian Rigid Monoidal Categoryabelian rigid monoidal category, Abelianabelian?

Is the Drinfeld-Majid center of an abelian rigid monoidal category, abelian? [stated in 1J of “ON THE CENTER OF FUSION CATEGORIES”On the center of fusion categories" by BruiguièresBruguières and Virelizier]Virelizier (link at Virelizier's page)]

In particular, I’m not seeing why any monomorphism in the center would have to be a kernel of a morphism? (I’m relatively happy with the other axioms holding, but if anyone has a reference where this is discuss explicitly, it’s appreciated )

Is the Center of an Abelian Rigid Monoidal Category, Abelian?

Is the Drinfeld-Majid center of an abelian rigid monoidal category, abelian? [stated in 1J of “ON THE CENTER OF FUSION CATEGORIES” by Bruiguières and Virelizier]

In particular, I’m not seeing why any monomorphism in the center would have to be a kernel of a morphism? (I’m relatively happy with the other axioms holding, but if anyone has a reference where this is discuss explicitly, it’s appreciated )

Is the center of an abelian rigid monoidal category, abelian?

Is the Drinfeld-Majid center of an abelian rigid monoidal category, abelian? [stated in 1J of On the center of fusion categories" by Bruguières and Virelizier (link at Virelizier's page)]

In particular, I’m not seeing why any monomorphism in the center would have to be a kernel of a morphism? (I’m relatively happy with the other axioms holding, but if anyone has a reference where this is discuss explicitly, it’s appreciated )

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AMaths
AMaths
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Is the Center of an Abelian Rigid Monoidal Category, Abelian?

Is the Drinfeld-Majid center of an abelian rigid monoidal category, abelian? [stated in 1J of “ON THE CENTER OF FUSION CATEGORIES” by Bruiguières and Virelizier]

In particular, I’m not seeing why any monomorphism in the center would have to be a kernel of a morphism? (I’m relatively happy with the other axioms holding, but if anyone has a reference where this is discuss explicitly, it’s appreciated )