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How to pronounce “injective”

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Pronunciation guide for injective

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Definition summary: (mathematics) Of, 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

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[Adjective]
(mathematics) Of, 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
(algebra, module theory, of a (left) module
M
{\displaystyle M}
over a ring
R
{\displaystyle R}
) Loosely, 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.
(category theory, most generally, of an object
Q
{\displaystyle Q}
in a category
C
{\displaystyle C}
) Loosely, 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.
(homological algebra, of a resolution) Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).