Injectivity is essential when studying the correctness of authentication protocols, because non-injective protocols may suffer from replay attacks. The standard ways of verifying injectivity either make use of a counting argument, which only seems to be applicable in a verification methodology based on model-checking, or draw conclusions on the basis of the details of the data-model used. We pr...

‎For the subclasses $mathcal{M}_1$ and $mathcal{M}_2$ of‎ ‎monomorphisms in a concrete category $mathcal{C}$‎, ‎if $mathcal‎{M}_2subseteq mathcal{M}_1$‎, ‎then $mathcal{M}_1$-injectivity‎ ‎implies $mathcal{M}_2$-injectivity‎. ‎The Baer type criterion is about‎ ‎the converse of this fact‎. ‎In this paper‎, ‎we apply injectivity to the classes of $C$-dense‎, ‎$C$-closed‎ ‎monomorphisms‎. ‎The con...

Using Escardó-Flagg approach to injectivity via Kock-Zöberlein monads in T0 topological spaces [3], and Hofmann’s recent study of injectivity for spaces [4], we characterize continuous maps which are injective with respect to special classes of embeddings using convergence: see [1]. In fact, convergence has been shown to be very useful in the characterization of special classes of maps, like ef...

We treat a relative version of the main theorem in [F2]: A transcendental approach to Kollár’s injectivity theorem. More explicitly, we give a curvature condition that implies Kollár type cohomology injectivity theorems in the relative setting. To carry out this generalization, we use Ohsawa-Takegoshi’s twisted version of Nakano’s identity.

This report describes a strong connection between maximum satisfiability and minimally-unsatisfiable subfor-mulas of any constraint system, as well as techniques for exploiting it. Focusing on CNF formulas, we explore this relationship and present novel algorithms for extracting minimally-unsatisfiable subformulas, including one that finds all such subformulas. We present experimental results s...

In a locally λ-presentable category, with λ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are λ-presentable, are known to be characterized by their closure under products, λ-directed colimits and λ-pure subobjects. Replacing the strict commutativity of diagrams by “commutativity up to ε”, this paper provides an “appro...

‎for the subclasses ${mathcal m}_1$ and ${mathcal m}_2$ of‎‎monomorphisms in a concrete category $mathcal c$‎, ‎if ${mathcal‎‎m}_2subseteq {mathcal m}_1$‎, ‎then ${mathcal m}_1$-injectivity‎‎implies ${mathcal m}_2$-injectivity‎. ‎the baer type criterion is about‎ ‎the converse of this fact‎. ‎in this paper‎, ‎we apply injectivity to the classes of {it $c$-dense‎, ‎$c$-closed}‎ ‎monomorphisms‎. ...

‎In this paper some properties of weak regular injectivity for $S$-posets‎, ‎where $S$ is a pomonoid‎, ‎are studied‎. ‎The behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎Also‎, ‎some‎ ‎characterizations of pomonoids over which all $S$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎Further‎, ‎we‎ ‎giv...