AI 中文总结
该注记刻画了有界 hoop 范畴的共扩展态射，证明了有界 Wajsberg hoop 等相关范畴的共扩展性，还导出了$\boldsymbol{Heyt}$与$\boldsymbol{MV}$范畴的共扩展性。
AI 中文摘要
本注记的主要目的是给出有界 hoop 范畴中共扩展态射的刻画，该刻画随后被用于证明若干有界 hoop 范畴作为范畴是共扩展的，其中包括有界 Wajsberg hoop 的簇，或更一般地，有界∨-hoop 的簇。该刻画还导出了 Heyting 代数范畴（记为$\boldsymbol{Heyt}$）的共扩展性，并恢复了 MV 代数范畴（记为$\boldsymbol{MV}$）已知的共扩展性。
英文摘要
The main aim of this note is to provide a characterisation of coextensive morphisms in the category of bounded hoops. This characterisation is then used to show that several categories of bounded hoops are coextensive as categories. Among these are the variety of bounded Wajsberg hoops, or more generally the variety of bounded $\vee$-hoops. Our characterisation also yields the coextensivity of the category $\mathbf{Heyt}$ of Heyting algebras and recovers the known coextensivity of the category $\mathbf{MV}$ of MV-algebras.
Comments9 pages;
