We introduce a new bicategorical model of linear logic based on profunctors between groupoids. This model is a new variation of the usual bicategory of profunctors, obtained by endowing groupoids with additional structure to constrain the profunctors. One goal of this new model is to provide a formal bridge between the model of finitary polynomial functors, also known as normal functors, and the combinatorial theory of generalized species of structures. Our approach consists in viewing finitary polynomial functors as analytic functors generated by free generalized species. The main conceptual novelty is the notion of kit, designed to control the extent to which species are free. We study kits from both combinatorial and logical perspectives. Profunctors that respect the kit structure are called stabilized, and the bicategory of stabilized profunctors gives rise to stable species of structures, a cartesian closed bicategory that embeds finitary polynomial functors. Stabilized profunctors and stable species can be given an extensional presentation as certain functors between subcategories of presheaves determined by the kit. This gives a strict 2-categorical presentation of the same model.
翻译:我们引入了一种新的双分类线性逻辑新模型, 其基础是群类之间的分辨。 这个模型是常见的双类分辨线性逻辑的新变异, 由使用附加结构来限制分辨的分解器获得。 这个新模型的一个目标是提供一个正式的桥梁, 连接有鳍的多胞菌杀菌者的模式, 也称为普通杀菌者, 和结构的通用物种组合理论。 我们的方法包括将有鳍的多胞胎杀菌者作为自由的通用物种产生的解析性杀菌者。 主要的理论创新是包的概念, 旨在控制物种自由的程度。 我们从组合和逻辑角度研究包包。 尊重包结构的教授被称作稳定, 稳定的活菌者两类产生稳定的结构物种种类。 一种卡提亚类封闭型双类, 嵌入有鳍的多胞胎真菌类。 稳定的前导体和稳定的物种的组合体概念性新概念概念是用来控制物种自由的范围。 我们从组合和逻辑角度研究包体结构结构结构的包件, 被确定为一种固定的分级的分级的分体。 。</s>