Relative Properties of Frame Language

The paper discusses semalltics of encodings in logical frameworkswhere equalities in object calculi are represented by families of types as the case inELF. The notion of Leibniz equality in a category is introduced. Two morphisms ina category are Leibniz equal if they are seen so by an internal category. The usualcategorical properties are then relativized to r-properties by requiring mediatingmorphisms to be unique up to some Leibniz equality. Using these terminologies,it is shown, by an example, that the …