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It is not a big risk to say that the class of surjective epimorphisns is big enough if we dfeal with classical problems of the theory of total algebras. None of the basio concepts and fundamental theorems needs others then surjeotive epis. Only in some special varieties non-surjeotive epis are considered -for example, localizations in the theory of rings. In our .opinion among all reasons of it the most important are the following, rirst -each •pi in a category of all algebras of a given typedoi:10.1515/dema-1987-1-215 fatcat:sbxuerzmojdh5ibbnd5ppiffpm