双线性扩张范畴

Double-linear Extension Categories

双线性扩张范畴C=A[M,N,φ,ψ]B的模范畴C Mod是双扩张代数的自然推广,且等价于四元组范畴C T.作为应用,给出了2-循环复形范畴与特殊的双扩张范畴等价的证明,以及由范畴A或B中的某些AR-序列可得C T中的部分AR序列.

The notion of the left module category over k-linear double-extension categories is a generalization of a double-extension algebra, and it is isomphie to the quadruple category ,eft.. As a main application of the result we use a special double-extension category to describe a 2-cycle complex category. And more, from some Austander-Reiten sequences in A or B we can obtain some Auslander- Reiten sequences in the corresponding quadruple category eF.