标题： 层拓扑斯理论：拉格朗日场论的一个强大框架 显示英文标题

标题： Sheaf Topos Theory: A powerful setting for Lagrangian Field Theory

摘要： 我们对经典场论的层拓扑理论描述进行了初步阐述，其动机是严格描述（无限维）场论空间的变分法 $\bf{(i)}$和经典费米子场空间的非平凡性，$\bf(ii)$ 这些考虑自然引出了超光滑集层拓扑理论的定义。 最后，我们指出了场空间无穷小结构描述以及（高阶）规范场的非微扰描述所必需的自然推广。 显示英文摘要

摘要： We provide an introductory exposition to the sheaf topos theoretic description of classical field theory motivated by the rigorous description of both $\bf{(i)}$ the variational calculus of (infinite dimensional) field-theoretic spaces, and $\bf(ii)$ the non-triviality of classical fermionic field spaces. These considerations naturally lead to the definition of the sheaf topos of super smooth sets. We close by indicating natural generalizations necessary to include to the description of infinitesimal structure of field spaces and further the non-perturbative description of (higher) gauge fields.