论文标题
基本托托伊
Elementary topoi
论文作者
论文摘要
作为原型类别，$ \ mathbf {set} $具有许多属性，使其在类别之间具有特殊性。从数学逻辑的角度来看，这样的属性之一就是$ \ mathbf {set} $具有足够的结构来“正确”正式化逻辑。但是，我们可能会问在另一个类别中形式化逻辑$ \ mathbf {c} $这可能是什么意思。 （基础）topos的概念提炼了$ \ mathbf {set} $的基本功能，这使我们能够执行此操作。该说明性报告定义了Topoi，并描述了Topos中一阶逻辑和设置理论的发展。
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise logic. However, we could ask what it might mean to formalise logic in another category $\mathbf{C}$. The notion of an (elementary) topos distills the essential features of $\mathbf{Set}$ which allow us to do this. This expository report defines topoi, and describes the development of first-order logic and set theory within a topos.
