K-finite decidable objects and finite cardinals in an arbitrary topos

In an elemetary topos $\varepsilo$, we prove that the class of K-finite decidable objects is the same to the class of finite cardinals in E if and only if every K-finite decidable object X such that $X \longrightarrow 1$ is epic, then $1 \longrightarrow X $ is split epic.

Main Author: Acuña Ortega, Osvaldo
Format: Artículo
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/2101
http://hdl.handle.net/10669/13003
Summary: In an elemetary topos $\varepsilo$, we prove that the class of K-finite decidable objects is the same to the class of finite cardinals in E if and only if every K-finite decidable object X such that $X \longrightarrow 1$ is epic, then $1 \longrightarrow X $ is split epic.