injective

1. 1.

   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

   属于或关于单射的:使像(或值域)中的每个元素至多与一个原像(或定义域)中的元素相关联；逆决定的。

2. 2.

   Loosely, having a certain generalizing property, abstracted from the study of Q as a Z-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module.

   非正式地,具有某种概括性质,源自将Q作为Z-模的研究。正式地,使得任何以M为起点的(左)R-模短正合序列可分裂,或若干等价陈述之一；参见“内射模”。

3. 3.

   Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism f:X→Y in C, for every morphism g:X→Q there exists a morphism h:Y→Q such that h∘f=g; see Injective object.

   粗略地说,具有与内射模类似的性质(见上)；正式地说,若给定范畴C中的单态射f:X→Y,对每个态射g:X→Q,存在态射h:Y→Q使h∘f=g；参见内射对象。

4. 4.

   Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).

   使得分解中涉及的(通常为模的)对象在上述代数意义下是内射的。

非正式地,具有某种概括性质,源自将Q作为Z-模的研究。正式地,使得任何以M为起点的(左)R-模短正合序列可分裂,或若干等价陈述之一；参见“内射模”。；粗略地说,具有与内射模类似的性质(见上)；正式地说,若给定范畴C中的单态射f:X→Y,对每个态射g:X→Q,存在态射h:Y→Q使h∘f=g；参见内射对象。；使得分解中涉及的(通常为模的)对象在上述代数意义下是内射的。；内射；单射