**Yoshifumi Tsuchimoto**

- A morphism
in a category is said to be
**monic**if for any object of and for any morphism , we have - A morphism
in a category is said to be
**epic**if for any object of and for any morphism , we have

- :monic .
- :epic .

- An object
in
is said to be
**injective**if it satisfies the following condition: For any morphism and for any monic morphism , ``extends'' to a morphism . - An object
in
is said to be
**projective**if it satisfies the following condition: For any morphism and for any epic morphism , ``lifts'' to a morphism .

- is a direct summand of free modules.
- is projective

is epic.