Cofree objects in the centralizer and the center categories

Document Type : Research Paper


Department of Mathematics, The University of Iowa (and University of Thi-Qar), 14 MacLean Hall, 52242-1419, Iowa City, Iowa, USA.


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 monidal categories. Most importantly, we investigate cofree objects of comonoids in these monoidal categories.


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