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...

Concurrent separation logic is distinguished by transfer of state ownership upon parallel composition and framing. The algebraic structure that underpins partial commutative monoids (PCMs). Extant research considers primarily from the logical perspective while comparatively less attention drawn to considerations. This paper provides an formalization in concurrent means structure-preserving func...

In a triangulated category, cofibre fill-ins always exist. Neeman showed that there is at least one "good" fill-in, i.e., whose mapping cone exact. Verdier constructed fill-in of particular form in his proof the $4 \times 4$ lemma, which we call "Verdier good". We show for several classes morphisms exact triangles, notions good and agree. prove lifting criterion commutative squares terms (Verdi...