Generalizing substitution
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 4, pp. 315-336.

It is well known that, given an endofunctor H on a category , 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 [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), 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 such that the functors T ' (-,X) uniformly carry a monad structure.

DOI : https://doi.org/10.1051/ita:2003022
Classification : 08B20,  18C15,  18C50
Mots clés : algebras of terms, non-wellfounded terms, substitution, iteration of guarded substitution rules, monads, hyperfunctions, finitely or possibly infinitely branching trees
@article{ITA_2003__37_4_315_0,
     author = {Uustalu, Tarmo},
     title = {Generalizing substitution},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {315--336},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {4},
     year = {2003},
     doi = {10.1051/ita:2003022},
     zbl = {1042.18003},
     mrnumber = {2053030},
     language = {en},
     url = {www.numdam.org/item/ITA_2003__37_4_315_0/}
}
Uustalu, Tarmo. Generalizing substitution. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 4, pp. 315-336. doi : 10.1051/ita:2003022. http://www.numdam.org/item/ITA_2003__37_4_315_0/

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