原可加函子、导挠理论与同调
Protoadditive functors, derived torsion theories and homology
摘要：
原可加函子被设计用来在非阿贝尔设置中替换可加函子。他们的性质进行了研究，特别是在与扭转理论，伽罗瓦论，同源性和因子分解系统。它示出了如何一个原添加剂无挠反射诱导链的派生扭转理论的类别中的更高的扩展，类似于伽罗瓦结构的更高的中央扩展先前考虑在半阿贝尔同调代数。这种更高的中心扩展也进行了研究，就伯克霍夫子范畴的反射器是protoadditive，或更一般地说，通过一个protoadditive反射器的因素。这样，我们通过高阶Hopf公式得到了反射体的非交换导出函子的简单描述.各种例子被认为是在类别的群体，紧凑的群体，内部群胚在半阿贝尔范畴，和其他的。
英文摘要：
Protoadditive functors are designed to replace additive functors in a non-abelian setting. Their properties are studied, in particular in relationship with torsion theories, Galois theory, homology and factorisation systems. It is shown how a protoadditive torsion-free reflector induces a chain of derived torsion theories in the categories of higher extensions, similar to the Galois structures of higher central extensions previously considered in semi-abelian homological algebra. Such higher central extensions are also studied, with respect to Birkhoff subcategories whose reflector is protoadditive or, more generally, factors through a protoadditive reflector. In this way we obtain simple descriptions of the non-abelian derived functors of the reflectors via higher Hopf formulae. Various examples are considered in the categories of groups, compact groups, internal groupoids in a semi-abelian category, and other ones.
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