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We study centrality of morphisms in a setting derived from that of a pointedcategory in which binary products commute with coequalisers. The main resultsof this paper show that much of the behaviour of central morphisms for unitalcategories is retained in our setting, including categories which are (weakly)unital, but also categories outside of the unital setting.

Centrality and the commutativity of finite products with coequalisers