A note on a category composition

N. Uglešić
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Abstract

The special properties of an abstract category morphism (for instance, being an identity, an isomorphism, an epimorphism., a monomorphism . . . ) fully depend on the category composition. Consequently, an isomorphic category to a concrete category may be not concrete, i.e., the concreteness is not a category invariant. Further, every small category is isomorphic to a small category whose objects are sets and whose morphisms are functions between those sets.
分类作文的注释
抽象范畴态射的特殊性质(如同构、同构、外射)。,单态…)完全取决于类别组成。因此,一个与具体范畴同构的范畴可能是不具体的,即具体性不是范畴不变量。更进一步,每一个小范畴都同构于一个小范畴,这个小范畴的对象是集合,而它们的态射是这些集合之间的函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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