Aczel-Mendler bisimulations are a coalgebraic extension of a variety of computational relations between systems. It is usual to assume that the underlying category satisfies some form of axiom of choice, so that the theory enjoys desirable properties, such as closure under composition. In this paper, we accommodate the definition in a general regular category -- which does not necessarily satisfy any form of axiom of choice. We show that this general definition 1) is closed under composition without using the axiom of choice, 2) coincide with other types of coalgebraic formulations under milder conditions, 3) coincide with the usual definition when the category has the regular axiom of choice. We then develop the particular case of toposes, where the formulation becomes nicer thanks to the power-object monad, and extend the formalism to simulations. Finally, we describe several examples in Stone spaces, toposes for name-passing, and modules over a ring.

翻译：Aczel-Mendler 模拟器是不同系统之间各种计算关系的凝固层延伸。 通常的假设是, 基础类别满足了某种选择的轴心, 因而理论具有可取的特性, 如组合中的封闭。 在本文中, 我们将定义纳入一般常规类别 -- -- 不一定满足任何形式的轴心。 我们显示, 这个一般性定义 1 是在没有使用选择的轴心的情况下, 组合封闭的, 2 与在较温和条件下的其他类型的煤热层配方相吻合, 3 与通常的定义相吻合, 当该类别有正常的轴心时, 3 与通常的定义相吻合。 然后我们发展了特定的例子, 即该配方由于有强力点的月球而变得更好, 并将形式主义扩大到模拟。 最后, 我们描述了在石空间的几个例子, 以使用名称和环上的模块为例 。</s>