AI 中文总结
该研究提供了理解格罗滕迪克拓扑斯的基础范畴论，阐述了Sites与Sheaves的性质并应用于模理论，还证明可构造普通范畴而非2-范畴的概型范畴。
AI 中文摘要
我们给出了理解格罗滕迪克拓扑斯的定义及应用所需的最低限度范畴论知识，阐述了 Sites（拓扑斯）与 Sheaves（层）的基本性质，并将其应用于模理论。我们证明，对于具有明确给定性质的范畴$\boldsymbol{C}$，可构造$\boldsymbol{C}$中对象的概型范畴，该范畴是普通范畴，而非栈情形下的2-范畴。
英文摘要
We give the minimum of category theory necessary for understanding the definition and applications of Grothendieck topos. We state the basic properties of sites and sheaves, and give applications to the theory of moduli. We prove that for categories $\mathbf C$ with explicit stated properties, we can construct a category of schemes of objects in $\mathbf C$ which is a proper category rather than a $2$-category as in the case of stacks.
