  This note is a part of the lecture notes of a graduate student algebraic
geometry seminar held at the department of mathematics in National Taiwan
Normal University, 2020 Falls. It aims to introduce an example of sheaves
defined on posets equipped with the Alexandrov topology, called the cellular
sheaves. A cellular sheaf is a functor from the category of a poset to the
category of specific algebraic structures (e.g. the category of groups).
Strictly speaking, even equipping the poset with the Alexandrov topology, it is
just the definition of a pre-sheaf on the Alexandrov topological space. By
checking details, cellular sheaves are actually sheaves on topological spaces.
This is a well-known fact in sheaf theory via the Kan extension, while it
requires readers who are familiar with the category theory. In this note, we
follow an elementary approach to describe the connection between cellular
sheaves and sheaves concerned in algebraic geometry, where only basic
commutative algebra and point-set topology are required as the background
knowledge.
