1982, Israel Program for Scientific Translations (translator), Lev J. Leifman (editor of translation), N. N. Čencov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Translations of Mathematical Monographs, Volume 53, page 50, 1° The composition of two morphisms is defined if and only if the final object of the first morphism is the initial object of the second. This composition is also a morphism, whose initial object is the initial object of the first morphism and whose final object is the final object of the second.
Source: wiktionary