Abstract

ABSTRACT. For the 2-monad ((−) 2,I,C)onCAT, with unit I described by identities and multiplication C described by composition, we show that a functor F: K2 � � K satisfying FIK =1K admits a unique, normal, pseudo-algebra structure for (−) 2 if and only if there is a mere natural isomorphism F · F 2 � � � F · CK. We show that when this is the case the set of all natural transformations F · F 2 � � F · CK formsa commutative monoid isomorphic to the centre of K. 1. Preliminaries 1.1. When we speak of ‘the 2-monad (−) 2 on CAT ’ we understand the canonical monad that arises by exponentiation of the cocommutative comonoid structure

Citations