Abstract
In the present paper we compare the concepts of monadic functors and functors with lifting and preservation properties which are essential in general algebra and in topological algebra. In doing this we show that the Linton conditions are sufficient for tripleability under milder assumptions as is known till yet. Using the concept of regular categories and regular functors [4] we give a complete generalization of theSet-based situation to a large class of base categories which admit certain factorizations.
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