schematic representation category objects ''x'' ''y'' ''z'' morphisms ''f'' ''g'' ''g'' ''f'' category 's three identity morphisms sub ''x'' sub sub ''y'' sub sub ''z'' sub explicitly represented would appear three arrows letters x z respectively '''category theory''' formalizes mathematical structure concepts terms labeled directed graph called ''category'' whose nodes called ''objects'' whose labelled directed edges called ''arrows'' morphisms category two basic properties ability compose arrows associatively existence identity arrow
Formal science Mathematics Pure mathematics Algebra Category theory