A definition of morphism
Topics
About: category
The table of contents of this article
Starting Context
- The reader knows a definition of category.
Target Context
- The reader will have a definition of morphism.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Definition
For any ordered pair of objects, \((O_1, O_2)\), an arrow, \(O_1 \rightarrow O_2\)
2: Note
Typically, an object is a set, and a morphism is a map, but they are generalized to be not necessarily so.
So, in general, "object" is just vaguely an object and "arrow" is just vaguely an arrow.
Usually, a morphism is called so as an element of a category.
