We present ICAR, a mathematical framework derived from category theory for representing cybersecurity NIST and MITRE's ontologies. Designed for cybersecurity, ICAR is a category whose objects are cybersecurity knowledge (weakness, vulnerability, impacted product, attack technique, etc.) and whose morphisms are relations between this knowledge, that make sense for cybersecurity. Within this rigorous and unified framework, we obtain a knowledge graph capable of identifying the attack and weakness structures of an IS, at the interface between description logics, database theory and cybersecurity. We then define ten cybersecurity queries to help understand the risks incurred by IS and organise their defence.

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