{'fraction_non_alphanumeric': 0.015017667844522967, 'fraction_numerical': 0.0, 'mean_word_length': 5.625730994152047, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Conditions for Interoperability

Interoperability for information systems remains a challenge both at the semantic and organisational levels. The original three-level architecture for local databases needs to be replaced by a categorical four-level one based on concepts, constructions, schema types and data together with the mappings between them. Such an architecture provides natural closure as further levels are superfluous even in a global environment. The architecture is traversed by means of the Godement calculus: arrows may be composed at any level as well as across levles. The necessary and sufficient conditions for interoperability are satisfied by composable (formal) diagrams both for intension and extension in categories that are cartesian closed and locally cartesian closed. Methods like partial categories and sketches in schema design can benefit from Freyd’s punctured diagrams to identify precisely type-forcing natural transformations. Closure is better achieved in standard full categories. Global interoperability of extension can be achieved through semantic annotation but only if applied at run time.