Abstract We are interested in properties, especially injectivity (in the sense of category theory), ternary rings operators generated by certain subsets an inverse semigroup via regular representation. determine all extended bicyclic which closed under triple product $$xy^*z$$ x y <...

Recently, Cochran and Harvey defined torsion-free derived series of groups and proved an injectivity theorem on the associated torsion-free quotients. We show that there is a universal construction which extends such an injectivity theorem to an isomorphism theorem. Our result relates injectivity theorems to a certain homology localization of groups. In order to give a concrete combinatorial de...

Synthetic aperture radar (SAR) uses relative motion to produce fine resolution images from microwave frequencies and is a useful tool for regular monitoring and mapping applications. Unfortunately, if target distance is estimated poorly, then phase errors are incurred in the data, producing a blurry reconstruction of the image. In this thesis, we introduce a new multistatic methodology for dete...

Haskell, as implemented by the Glasgow Haskell Compiler (GHC), allows expressive type-level programming. The most popular typelevel programming extension is TypeFamilies , which allows users to write functions on types. Yet, using type functions can cripple type inference in certain situations. In particular, lack of injectivity in type functions means that GHC can never infer an instantiation ...

Haskell, as implemented by the Glasgow Haskell Compiler (GHC), allows expressive type-level programming. The most popular typelevel programming extension is TypeFamilies , which allows users to write functions on types. Yet, using type functions can cripple type inference in certain situations. In particular, lack of injectivity in type functions means that GHC can never infer an instantiation ...

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...