Centralizer and faithful groupoid (Q536161)

The author correlates existence and aspect of some properties of centralizers with the conceptual notion of \(\Theta\)-faithful objects in a category. Then, a large choice of examples from standard algebraic situations to topological models is produced. In particular, this allows to assert the existence of centralizers in some of of the new notions of algebras, as Leibniz algebras, introduced by \textit{J.-L. Loday} [Enseign. Math., II. Sér. 39, No.~3--4, 269--293 (1993; Zbl 0806.55009)], associated dialgebras [Dialgebras and related operads, Lect. Notes Math. 1763 (2001; Zbl 0970.00010)] and trialgebras [\textit{J.-L. Loday} and \textit{M. Ronco}, Contemp. Math. 346, 369--398 (2004; Zbl 1065.18007)].