definition of morphism
Topics
About: category
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
- 3: Note
Starting Context
- Nothing.
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: Structured Description
Here is the rules of Structured Description.
Entities:
\( O_1\): \(\in \{\text{ the objects }\}\)
\( O_2\): \(\in \{\text{ the objects }\}\)
\(*m\): \(: O_1 \to O_2\), \(\in \{\text{ the arrows from } O_1 \text{ to } O_2\}\)
Conditions:
//
2: Natural Language Description
For any ordered pair of objects, \((O_1, O_2)\), any arrow, \(m: O_1 \to O_2\)
3: Note
"What is "object" or "arrow"?" is a natural question, but 'object' is any entity and 'arrow' is anything that connects any 2 objects with any direction.
Typically, an object is a set, and a morphism is a map, but they are generalized to be not necessarily so.
Usually, a morphism is called so as an ingredient of a category.
