Definitions
1.AdjectiveOf, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic
2.AdjectiveLoosely, having a certain generalizing property, abstracted from the study of
Q
{\displaystyle \mathbb {Q} }
as a
Z
{\displaystyle \mathbb {Z} }
-module. Formally, such that any short exact sequence of (left)
R
{\displaystyle R}
-modules beginning with
M
{\displaystyle M}
splits, or any of several equivalent statements: See Injective module.
3.AdjectiveLoosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism
f
:
X
→
Y
{\displaystyle f:X\to Y}
in
C
{\displaystyle C}
, for every morphism
g
:
X
→
Q
{\displaystyle g:X\to Q}
there exists a morphism
h
:
Y
→
Q
{\displaystyle h:Y\to Q}
such that
h
∘
f
=
g
{\displaystyle h\circ f=g}
; see Injective object.
4.AdjectiveSuch that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).