In a previous work we have investigated the world of TreeL-categories, where L is a meetsemilattice monoid, with particular attention to lifting factorization properties for TreeL-functors. Our method consisted in lifting constructions as far as possible through the different levels of our structures, namely: the lp 2-category L, the monoidal category TreeL of symmetric L- categories and TreeL-Cat. We did apply the same method to the factorization reflection property in order to shift Conduch´e’s theorem in this enriched setting. In this context we did prove the equivalence between the existence of a right adjoint to the inverse image functor and the factorization reflection property. The further condition imposing that we have to consider only Conduch´e enrichments is trivially satisfied in the Set case, when enriched categories are ordinary categories. In fact Set is a category of trees on the trivial meet-semilattice monoid I, freely generated by the empty set [17]. There, no factorization in the sense of Definition 2 is possible. TreeL-categories are particularly useful in modeling non-deterministic concurrent processes; in particular BehL is a powerful tool to represent operational semantics, both in the case of interleaving and true concurrent approach.

The notion of state and models for interaction, categorically / S. Kasangian, A. Labella, A. Montoli. - roma : Università di Roma “La Sapienza” Dipartimento di Informatica, 2008.

### The notion of state and models for interaction, categorically

#### Abstract

In a previous work we have investigated the world of TreeL-categories, where L is a meetsemilattice monoid, with particular attention to lifting factorization properties for TreeL-functors. Our method consisted in lifting constructions as far as possible through the different levels of our structures, namely: the lp 2-category L, the monoidal category TreeL of symmetric L- categories and TreeL-Cat. We did apply the same method to the factorization reflection property in order to shift Conduch´e’s theorem in this enriched setting. In this context we did prove the equivalence between the existence of a right adjoint to the inverse image functor and the factorization reflection property. The further condition imposing that we have to consider only Conduch´e enrichments is trivially satisfied in the Set case, when enriched categories are ordinary categories. In fact Set is a category of trees on the trivial meet-semilattice monoid I, freely generated by the empty set [17]. There, no factorization in the sense of Definition 2 is possible. TreeL-categories are particularly useful in modeling non-deterministic concurrent processes; in particular BehL is a powerful tool to represent operational semantics, both in the case of interleaving and true concurrent approach.
##### Scheda breve Scheda completa Scheda completa (DC)
concurrency ; category theory
Settore INF/01 - Informatica
Dipartimento di Informatica, Università di Roma “La Sapienza”
Working Paper
The notion of state and models for interaction, categorically / S. Kasangian, A. Labella, A. Montoli. - roma : Università di Roma “La Sapienza” Dipartimento di Informatica, 2008.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/40107`
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