2,131 research outputs found
From Proof Nets to the Free *-Autonomous Category
In the first part of this paper we present a theory of proof nets for full
multiplicative linear logic, including the two units. It naturally extends the
well-known theory of unit-free multiplicative proof nets. A linking is no
longer a set of axiom links but a tree in which the axiom links are subtrees.
These trees will be identified according to an equivalence relation based on a
simple form of graph rewriting. We show the standard results of
sequentialization and strong normalization of cut elimination. In the second
part of the paper we show that the identifications enforced on proofs are such
that the class of two-conclusion proof nets defines the free *-autonomous
category.Comment: LaTeX, 44 pages, final version for LMCS; v2: updated bibliograph
Elliptic Operators and Higher Signatures
Building on the theory of elliptic operators, we give a unified treatment of
the following topics:
- the problem of homotopy invariance of Novikov's higher signatures on closed
manifolds;
- the problem of cut-and-paste invariance of Novikov's higher signatures on
closed manifolds;
- the problem of defining higher signatures on manifolds with boundary and
proving their homotopy invariance.Comment: 54 pages. Survey-article. Related papers can be retrieved from
http://www.mat.uniroma1.it/people/piazz
ω-Inductive completion of monoidal categories and infinite petri net computations
There exists a KZ-doctrine on the 2-category of the locally small categories whose algebras are exactly the categories which admits all the colimits indexed by ω-chains. The paper presents a wide survey of this topic. In addition, we show that this chain cocompletion KZ-doctrine lifts smoothly to KZ-doctrines on (many variations of) the 2-categories of monoidal and symmetric monoidal categories, thus yielding a universal construction of colimits of ω-chains in those categories. Since the processes of Petri nets may be axiomatized in terms of symmetric monoidal categories this result provides a universal construction of the algebra of infinite processes of a Petri net
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