This is an overview on certain higher structural constructions in physics. Main motivations of our current attempt are as follows: (i) to provide a brief introduction to the basics of derived algebraic geometry, (ii) to understand how certain derived objects naturally appear in physics and give rise to a formal mathematical treatment, and (iii) to investigate how the notion of a factorization algebra together with certain higher categorical structures come into play to encode the structure of observables in physics. Adopting such a heavy and relatively enriched language allows us to formalize the notions of quantization and observables in quantum field theory as well. This document is organized to explain the underlying mathematical treatment for each task in an expository manner.

这是对物理学中某些更高结构结构的概述。我们当前尝试的主要动机如下：（i）简要介绍派生代数几何的基础知识，（ii）了解某些派生对象如何自然地出现在物理学中并产生正式的数学处理，以及（ iii) 研究分解代数的概念如何与某些更高的分类结构一起发挥作用来编码物理学中可观测量的结构。采用如此繁重且相对丰富的语言使我们能够形式化量化和可观察的概念在量子场论中也是如此。本文档旨在以说明性的方式解释每个任务的基本数学处理。