It is well known that, given an endofunctor on a category , the initial -algebras (if existing), i.e., the algebras of (wellfounded) -terms over different variable supplies , give rise to a monad with substitution as the extension operation (the free monad induced by the functor ). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness),...
It is well known that, given an endofunctor on a category ,
the initial -algebras (if existing), , the algebras
of (wellfounded) -terms over different variable supplies ,
give rise to a monad with substitution as the extension operation
(the free monad induced by the functor ). Moss [17]
and Aczel, Adámek, Milius and Velebil [12] have shown
that a similar monad, which even enjoys the additional special
property of having iterations for all guarded substitution rules
(complete iterativeness),...
The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18–32],...
The question of how to combine monads arises naturally in many areas
with much recent interest focusing on the coproduct of two monads.
In general, the coproduct of arbitrary monads does not always exist.
Although a rather general construction was given by
Kelly [
(1980) 1–83], its generality is reflected in its
complexity which limits the applicability of this construction.
Following our own research [C. Lüth and N. Ghani,
(2002) 18–32], and that of
Hyland,...
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