Restriction categories II: Partial map classification
J.R.B. Cockett and Stephen Lack
An algebraic characterization of monads which are abstract partial
map classifiers is provided, without the assumption that the
categories in question possess products. By an abstract partial map
classifier we mean a monad whose Kleisli category is a full subcategory
of a partial map category wherein the induced comonad classifies partial
maps in the usual sense. A construction of the corresponding
actual partial map classifier from an abstract one is described, and
conditions for an abstract partial map classifier to be a real one are
The paper uses the notion of a restriction category developed in
earlier work, and the characterization of these as
full subcategories of partial map categories.
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Last modified: Wed Oct 25 11:49:44 EST 2000