Applied Categorical Structures

, Volume 22, Issue 5–6, pp 833–856 | Cite as

Two Ways to Centralizers of Equivalence Relations



We investigate what is the common part of the action accessible and the fibrewise algebraically cartesian closed (facc) categories dealing with the existence of centralizers of equivalence relations. Doing this, we shall introduce some new aspects of the Beck-Chevalley commutation with respect to the fibration of points \(\P _{\mathbb C}\) and shall characterize the existence of those centralizers by a specific property of this same fibration.


Fibration of points Beck-Chevalley commutation Centralizer Unital, Mal’cev and protomodular categories Action accessible and fiberwise algebraically cartesian closed categories 

Mathematics Subject Classification (2010)

18A40 18C15 18D15 20A05 13A99 17B99 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du LittoralCalais CedexFrance

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