自由生成小范畴的第一Baues-Wirsching上同调的计算
On computation of the first Baues--Wirsching cohomology of a freely-generated small category
摘要：
Baues-Wirsching上同调是小范畴的上同调之一。我们的目的是描述由有限自由生成的小范畴的第一Baues-Wirsching上同调。我们考虑的情况下，系数是一个自然的系统所获得的函子和目标函子的组合。给出了一个求内导子向量空间生成元的算法。已知存在从小范畴的导子向量空间到以内导子向量空间为核的第一Baues-Wirsching上同调的满射。
英文摘要：
The Baues--Wirsching cohomology is one of the cohomologies of a small category. Our aim is to describe the first Baues--Wirsching cohomology of the small category generated by a finite quiver freely. We consider the case where the coefficient is a natural system obtained by the composition of a functor and the target functor. We give an algorithm to obtain generators of the vector space of inner derivations. It is known that there exists a surjection from the vector space of derivations of the small category to the first Baues--Wirsching cohomology whose kernel is the vector space of inner derivations.
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