The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets generalising the original application to suggest that Petri nets with different kinds of transitions can be modelled in the same categorical framework. Transitions representing truth-values, probabilities, rates or multiplicities, evaluated in different algebraic structures called lineales are useful and are modelled here in the same category. We investigate (categorical instances of) this generalised model and its connections to more recent models of categorical nets.

翻译：Petri网的范畴建模近来备受关注。Dialectica构造同样获得了应有的重视。我们重新审视了将Dialectica构造作为Petri网范畴模型的原始应用，通过泛化这一应用指出，包含不同类型变迁的Petri网可在同一范畴框架下建模。表征真值、概率、速率或多重性的变迁（其取值在称为"线性代数"的不同代数结构中进行评估）具有实用价值，并在本文中于同一范畴内实现建模。我们研究了该泛化模型（的范畴实例）及其与最新范畴网模型之间的关联。