On computation of the first Baues--Wirsching cohomology of a freely-generated small category

Yasuhiro Momose; Yasuhide Numata

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arXiv · 1402.6085

On computation of the first Baues--Wirsching cohomology of a freely-generated small category

Yasuhiro Momose·Yasuhide Numata

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Abstract

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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Yasuhiro Momose, Yasuhide Numata. 2014-02-25. On computation of the first Baues--Wirsching cohomology of a freely-generated small category. https://arxiv.org/abs/1402.6085

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