The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. An important class of multiplicative Petri net morphisms is also identified. Th...

Continuous lattices were characterised by Mart́ın Escardó as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. An example: ω-CPO’s are precisely the posets that are Kan-injective w.r.t. the embeddings ω →֒ ω + 1 and 0 →֒ 1. For every class H of morphisms we study the subcategory of all objects Kan-in...

This paper studies the ambiguity of morphisms in free monoids. A morphism σ is said to be ambiguous with respect to a string α if there exists a morphism τ which differs from σ for a symbol occurring in α, but nevertheless satisfies τ(α) = σ(α); if there is no such τ then σ is called unambiguous. Motivated by the recent initial paper on the ambiguity of morphisms, we introduce the definition of...

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...

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-...

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...

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.

To every regular category $\mathcal{A}$ equipped with a degree function $\delta$ one can attach pseudo-abelian tensor $\mathcal{T}(\mathcal{A},\delta)$. We show that the generating objects of $\mathcal{T}$ decompose canonically as direct sum. In this paper we calculate morphisms, compositions morphisms and products summands. As special case recover original construction Deligne's $\operatorname...

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...

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...