Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 14 1 2021 01 01 Cofree objects in the centralizer and the center categories 1 38 100669 10.29252/cgasa.14.1.1 EN Adnan H. Abdulwahid Department of Mathematics, The University of Iowa (and University of Thi-Qar), 14 MacLean Hall, 52242-1419, Iowa City, Iowa, USA. Journal Article 2021 01 31 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. https://cgasa.sbu.ac.ir/article_100669_4c34698930621a134561e3dada358da3.pdf