The early controversies surrounding the axiom of choice are well known, as are the many results that followed concerning its (in)dependence from, and equivalence to, other mathematical propositions. This paper focuses not on the logical status of the axiom but rather on showing why it fails in certain categories.

中文翻译：

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为什么选择公理有时会失败

关于选择公理的早期争议是众所周知的，随之而来的许多关于选择公理（与其他数学命题的依赖性）的结果也众所周知。本文不着重于公理的逻辑状态，而是着重说明为什么它在某些类别中会失败。