Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two different categories may also be considered "equivalent" for purposes of category theory, even if they do not have precisely the same structure.
two categories are the same if they have the same collection of objects the same collection of arrows and the same associative method of composing any pair of arrows two different categories may also be considered "equivalent" for purposes of category theory even if they do not have precisely the same structure