3 Use markdown enumerations, just for fun

It seems that there are many definitions of quasi coherent sheaves(modules). There is a nice page on nLab quasi coherent sheaves

My questions are:

1

1. Are there any other definitions of quasi coherent sheaves? For what?(I mean in which situation, they should be redefined to satisfy the working environment)

2.How

2. How are they related?

For question 2.nLab said 2, nLab says these definitions are equivalent.There equivalent. There are four definitions in nLab. It seems except first definitions, the other three are equivalent, just restate in different language: i.e presheaves <--->pseudo <---> pseudo functors <--->fibered <---> fibered categories.

But are these definitions exactly the same as the classical definitions? (as locally presentable modules)

2 added 97 characters in body

It seems that there are many definitions of quasi coherent sheaves(modules). There is a nice page on nLab quasi coherent sheaves

My questions are:

1 Are there any other definitions of quasi coherent sheaves? For what?(I mean in which situation, they should be redefined to satisfy the working environment)

2.How are they related?

For question 2. nLab 2.nLab said these definitions are equivalentequivalent.There are four definitions in nLab. But how It seems except first definitions, the other three are they equivalent? In which sense? Say, categorical equivalent or just restate in different language: i.e presheaves<--->pseudo functors<--->fibered categories.

But are these definitions exactly the same as the classical definitionsbut different ways to describe?I hope to get some explanations describing their relationship explicit (as locally presentable modules)

1

What are the relationship between various definitions for quasi coherent sheaves?

It seems that there are many definitions of quasi coherent sheaves(modules). There is a nice page on nLab quasi coherent sheaves

My questions are:

1 Are there any other definitions of quasi coherent sheaves? For what?(I mean in which situation, they should be redefined to satisfy the working environment)

2.How are they related?

For question 2. nLab said these definitions are equivalent. But how are they equivalent? In which sense? Say, categorical equivalent or exactly the same definitions but different ways to describe? I hope to get some explanations describing their relationship explicit