Coherence Completions of Categories and Their Enriched Softness
Hongde Hu, André Joyal · Electronic Notes in Theoretical Computer Science · 1997
We summarize some recent results on coherence completions of categories. Our goal is to demonstrate that there is a close connection between Girard's coherence spaces and free bicomplete categories. We extend coherence spaces to C-valued coherence spaces with an arbitrary category C, called the coherence completion of C, and study its enriched softness. We show that the coherence completion of C is monoidal closed, or ∗-autonomous when C is. The interpretation of the connectives of linear logic in the coherence completions provides a way to use the free bicompletions to capture semantics of linear logic.