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Note on total categories

Published online by Cambridge University Press:  17 April 2009

Walter Tholen
Fernuniversität, Postfach 940, D-5800 Hagen, Federal Republic of Germany.
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It is shown that, for a semi-topological functor T: A → X, the category A is total, that is, the Yoneda embedding of A has a left adjoint, if X is total. In particular, monadic categories over Set (possibly without rank) are total, and full reflective subcategories of total categories are total.

Research Article
Copyright © Australian Mathematical Society 1980


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