标题： 论态射的广延性 显示英文标题

标题： On extensivity of morphisms

摘要： 范畴的广泛性可以描述为范畴中余积的一个性质，即它们是不相交且普遍的。 另一种观点是，它是范畴中态射的一个性质。 本文通过一个自然的广泛和共广泛态射的概念来探讨这一观点。 通过这些概念，泛代数中的主题，如严格细化和Fraser-Horn性质，具有范畴形式，从而享受范畴一般化的优点。 另一方面，围绕这些主题的泛代数理论启发了范畴结果。 本文建立的一个结果是，一个Barr-精确范畴是共广泛的当且仅当该范畴中的每个分裂单射都是共广泛的。 显示英文摘要

摘要： Extensivity of a category may be described as a property of coproducts in the category, namely, that they are disjoint and universal. An alternative viewpoint is that it is a property of morphisms in a category. This paper explores this point of view through a natural notion of extensive and coextensive morphism. Through these notions, topics in universal algebra, such as the strict refinement and Fraser-Horn properties, take categorical form and thereby enjoy the benefits of categorical generalisation. On the other hand, the universal algebraic theory surrounding these topics inspire categorical results. One such result we establish in this paper is that a Barr-exact category is coextensive if and only if every split monomorphism in the category is coextensive.