<p> Triples and the categories of triple algebras are relativized by a full faithful functors. The Tripleability Theorem in [1] is correspondingly relativized. The concept of the rank of a triple becomes intrinsic in this setting. Preservation of non-existing limits is interpreted in terms of limit-colimit commutation property. This is used to account for the usual description of the category of algebras as the cateeory of all product preserving setvalued functors on the opposite category of free algebras. </p> / Thesis / Doctor of Philosophy (PhD)