Let W → C be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed the stack of expanded degenerations of W . We then constructed the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli spaces of stable morphisms associated to W/C. Using similar technique, for a pair of smooth varie...

A logic of orthogonality characterizes all “orthogonality consequences” of a given class Σ of morphisms, i.e. those morphisms s such that every object orthogonal to Σ is also orthogonal to s. A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes Σ of...

Software design implies searching for and establishing an adequate morphism between the real world and the desired software. Morphisms establish correspondences between different domains while some properties are preserved, at the same time. It allows seeing different things as the same, taking the substitute image for the real one. The more adjusted to reality the morphism is, the better the s...

Institutions were introduced by Goguen and Burstall [GB84, GB85, GB86, GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality bet...

In this paper we investigate the structure of most general kind substitution shifts, including non-minimal ones and allowing erasing morphisms. We prove decidability all properties these morphisms with respect to shift space generated by iteration, such as aperiodicity, recognizability, irreducibility or minimality.

The complexity of large system models in software engineering nowadays is mastered by using different views. View-based modeling aims at creating small, partial models, each one of them describing some aspect of the system. Existing formal techniques supporting view-based visual modeling are based on typed attributed graphs, where views are related by typed attributed graph morphisms. Such morp...

We describe the moduli space of morphisms between polarized abelian varieties. The discrete invariants, derived from a Poincaré decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in the decomposition. They are sufficient in order to detect the irreducible components for the moduli space of morphisms which are compatible with the polarizations.

The intention of the paper is to show how several categorical (open morphisms, path morphisms and coalgebraic morphisms based) approaches to an abstract characterization of bisimulation relate to each other and to behavioral bisimulations, in the setting of higher dimensional automata. Such a relating makes it possible to develop a metatheory designed for unified definition and study of equival...

We introduce a new concept in the area of formal logic: axioms for model morphisms. We work in the setting of specification languages that define the semantics of a theory as a category of models. While it is routine to use axioms to specify the class of models of a theory, there has so far been no analogue to systematically specify the morphisms between these models. This leads to subtle probl...