[Schemes III] 24 Hours on Morphisms of Local Types

In this post, we will study morphisms of local types, including quasi-compact morphism, morphism of locally finite type, and finite type morphism. Roughly speaking, for these kinds of morphisms, we often use tools from commutative algebra. In contrast, for morphisms of global type, i.e. separated morphism, geometric tools is often used. This note is short, but difficult, and important.