Generalizing substitution

Rannsóknarafurð: Framlag til fræðitímaritsGreinritrýni

28 Tilvitnanir (Scopus)

Útdráttur

It is well known that, given an endofunctor H on a. category C, the initial (A + H-)-algebras (if existing), i.e., the algebras of (wellfounded) H-terms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss and Aczel, Adámek, Milius and Velebil have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness), arises from the inverses of the final (A + H-)-coalgebras (if existing), i.e., the algebras of non-wellfounded H-terms. We show that, upon an appropriate generalization of the notion of substitution, the same can more generally be said about the initial T′(A, -)-algebras resp. the inverses of the final T′(A, -)-coalgebras for any endobifunctor T′ on any category C such that the functors T′(-, X) uniformly carry a monad structure.

Upprunalegt tungumálEnska
Síður (frá-til)315-336
Síðufjöldi22
FræðitímaritRAIRO - Theoretical Informatics and Applications
Bindi37
Númer tölublaðs4
DOI
ÚtgáfustaðaÚtgefið - 2003

Fingerprint

Sökktu þér í rannsóknarefni „Generalizing substitution“. Saman myndar þetta einstakt fingrafar.

Vitna í þetta