论文标题
$ \ mathsf {cat} $中的预验理论构成了群体类别和骨骼类别
Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$
论文作者
论文摘要
我们描述了小类类别中的预先理论：扭转对象是群体，而无扭转的对象是骨骼类别，即每个同构为自动形态的那些类别。我们从$ cat $中的两个意外属性中推断出这些结果，这些属性是识别对象对的：它们是忠实的，反映了同构。
We describe a pretorsion theory in the category $Cat$ of small categories: the torsion objects are the groupoids, while the torsion-free objects are the skeletal categories, i.e., those categories in which every isomorphism is an automorphism. We infer these results from two unexpected properties of coequalizers in $Cat$ that identify pairs of objects: they are faithful and reflect isomorphisms.
