A Double Category Theoretic Analysis of Graded Linear Exponential Comonads
Shin-ya Katsumata · Lecture notes in computer science · 2018
Graded linear exponential comonads are an extension of linear exponential comonads wih grading , and provide a categorical semantics of resource-sensitive exponential modality in linear logic. In this paper, we propose a concise double-category theoretic formulation of graded linear exponential comonads as a kind of monoid homomorphisms from the multiplicative monoids of semirings to the composition monoids of symmetric monoidal endofunctors. We also exploit this formulation to derive the category of graded comonoid-coalgebras, which decompose graded linear exponential comonads into symmetric monoidal adjunctions plus twists.