The Formal Theory of Hopf Algebras
نویسنده
چکیده
The category HopfC of Hopf monoids in a symmetric monoidal category C, assumed to be locally finitely presentable as a category, is analyzed with respect to its categorical properties. Assuming that the functors “tensor squaring” and “tensor cubing” on C preserve directed colimits one has the following results: (1) If, in C, extremal epimorphisms are stable under tensor squaring, then HopfC is locally presentable, coreflective in the category of bimonoids in C and comonadic over the category of monoids in C. (2) If, in C, extremal monomorphisms are stable under tensor squaring, then HopfC is locally presentable as well, reflective in the category of bimonoids in C and monadic over the category of comonoids in C. MSC 2000: Primary 16T05, Secondary 18D10
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