摘要
CD表示完全分配格与完备映射作成的范畴,则CD(以及Frm)仅有平凡格{0,1}作为(通常的)投射对象,而CD的正则投射对象恰是满足完全不变条件(11且aa_i(i∈J)a∧_(i∈J)a_i)的完备集环,这些正则投射对象及其间的保关系的完备映射还构成CD的一个余反射子范畴。
CD denotes the category of completely distributive lattices and complete maps. Then CD(as well as Frm) has only the trivial lattice {0, 1} as its (ordinary) projective objects. The regular projective objects of CD are exactly the completely stable complete rings of sets (completely stableness means: 11 and aa_i(i∈ J)a∧a_i). And these regular projective ob- jects with the complete maps preserving between them form a coreflective subcategory of CD.
关键词
完全分配格
范畴
正则投射
完全不变性
Completely distributive lattice
Category
Regular projectiveness
Completely stableness
