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By Bodo Pareigis

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106, 312 - 320, 1968. Anschrift des Verfassers: Prof. Dr. Bodo Pareigis, Mathematisches Institut der Universität, 8 München 13, Schellingstraße 2 - 8 .

Am. Math. Soc. 16, 544 - 546,1965. : Limit monads in categories. Aarhus Universitet Preprint series 1967/68 No. 6. : [1] Functorial semantics of algebraic theories. Thesis, Columbia University, 1963. - [2] Functorial semantics of algebraic theories. Proc. Nat. Acad. Sei. USA 50, 869 - 872, 1963. - [3] An elementary theory of the category of sets. Proc. Nat. Acad. Sei. USA 52, 1506 -1511, 1964. : Triples versus theories. Notices Am. Math. Soc. 13, 227, 1966. : A triple miscellany. Dissertation. Wesleyan University.

B. bei Limites, ist diese universelle Lösung bis auf Isomorphie eindeutig bestimmt. Daher ist es sinnvoll, das Vorliegen einer solchen universellen Lö­ sung mit einem besonderen Namen zu versehen. Definition: Ein Funktor © : X) -*(E heißt monadisch, wenn © einen linksadjungierten Funktor g : (E ->X) besitzt, so daß der durch die Monade (©$ = ξ), μ, e) definierte Funktor £ : X) -» & ein Isomorphismus ist. In bezug auf die algebraischen Kategorien und Funktoren gilt nun der folgende Satz. Satz 14: Jeder algebraische Funktor ist monadisch.

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