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Internal category

structure, with properties similar to a (small) category, constructed inside any category with pullbacks; two objects O (objects) and M (morphisms), equipped with arrows s, t: M → O (source/target), e: O → M (identity), m: M ₛ×ₜ M → M (composition)

Pronunciation
/ɪnˈtəːnəl ˈkatəɡəri/
/ɪnˈtərnl ˈkædəˌɡɔri/