拉回图中的函子

The Functors Arising from Pullback Diagram

设R1,R2,R′是三个环,j1:R1→R′和j2:R2→R′是环的同态,如果环R是j1,j2作为环的拉回,则称R是环R1和R2通过环R′的拉回环.首先证明拉回环R上的模范畴与以R1-模及R2-模为对象构造的一类范畴之间存在一对伴随对函子,其次给出模n剩余类环上的应用,证明了在模n剩余类环上这样的函子伴随对具有拟逆关系.

Given two homomorphisms of ringsj1：R1→R＇ and j2：R2→R＇ , a new ring R called the pullback of R1 and R2 over R＇ is constructed. Let F denote the category whose objects are the triples （M1, M2, α） where Mi∈Ri -Mod, i= 1,2, and a is an R＇-isomophism. The funtors P ： F→ R -Mod and S ： R -Mod→F are proved to be an adjoint pair and have quasi-inverse relation in the special case of the rings of residue classes of modulo integers.