Enriched positive logic

Abstract

Building on our previous work on enriched regular logic, we introduce an enriched version of positive logic and relate it to enriched cone-injectivity classes and enriched accessible categories. To do this, we need a factorization system on the base of enrichment in order to interpret existential quantification and disjunctions. We will also show how to treat unique existence in enriched logic, and how to relate it to local presentability.