Adnan Abdulwahid: Cofree objects in centralizer and center categories
We study cocompleteness, co-wellpoweredness and generators in the centralizer category of an object or morphism in a monoidal category, and the center or the weak center of a monoidal category. We explicitly give some answers for when colimits, cocompleteness, co-wellpoweredness and generators in these monoidal categories can be inherited from their base monoidal categories. Most importantly, we investigate cofree objects of comonoids in these monoidal categories.
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