Abstract

Hyperhomology is applied to give explicit constructions of left or right adjoint functors of some inclusions between unbounded homotopy categories of additive categories arising from cotorsion pairs in abelian categories. These constructions are independent of Brown representability and do not involve cardinality in set theory. Applications are then given to injective cotorsion pairs in abelian categories and some typical cotorsion pairs in module categories of rings.

中文翻译：

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超同调在伴随函子中的应用

摘要

超同调用于给出由阿贝尔范畴中的余量对产生的加性范畴的无界同伦范畴之间某些包含的左或右伴随函子的显式构造。这些结构独立于布朗可表示性，并且不涉及集合论中的基数。然后应用了阿贝尔范畴中的内射余量对和环模范畴中的一些典型余量对。