The focus of this paper is to endow step-wise modification of nets with refinement that preserves liveness. Modification of nets uses rules that allow substituting subnets of the left hand side by subnets of the right hand side of the rule. Such rules are then restricted so that the liveness is preserved. Rule-based modification is expressed in terms of spans of morphisms and two pushout constr...

Adámek and Sousa recently solved the problem of characterizing the subcategories K of a locally λ-presentable category C which are λ-orthogonal in C, using their concept of Kλ-pure morphism. We strenghten the latter definition, in order to obtain a characterization of the classes defined by orthogonality with respect to λ-presentable morphisms (where f :A B is called λ-presentable if it is a λ-...

We show that the category of Poisson manifolds and Poisson maps, the category of symplectic microgroupoids and lagrangian submicrogroupoids (as morphisms), and the category of monoids and monoid morphisms in the microsymplectic category are equivalent symmetric monoidal categories.

An algebraic deformation theory of coalgebra morphisms is constructed.

Morphisms to finite semigroups can be used for recognizing omega-regular languages. The socalled strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic morphism) and a trivial complementation procedure. We give a quadratic-time algorithm for computing the syntactic morphism from any given strongly recognizing morphi...

Let W/C be a degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first construct the stack of expanded degenerations of W . We then construct 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 a similar technique, for a pair (Z,D) of smooth v...

We study harmonic morphisms by placing them into the context of conformal foli-ations. Most of the results we obtain hold for bres of dimension one and codomains of dimension not equal to two. We consider foliations which produce harmonic mor-phisms on both compact and noncompact Riemannian manifolds. By using integral formulae, we prove an extension to one-dimensional foliations which produce ...