Question about commutative diagram

[seriously disabled]

In the commutative diagrams page in wolfram, what does the [math]\phi_{i_{0}}[/math] above the arrows mean?

[ajb]

In this context, [math]\phi_{i_{0}}: A_{i_{0}} \longrightarrow B_{i_{0}}[/math] is a map between the sets. It is often written as

 

[math]A_{i_{0}}\stackrel{\phi_{i_{0}}}{\longrightarrow} B_{i_{0}}[/math].

 

Does that help?

[seriously disabled]

Yes and thanks for the clarification ajb.

[ajb]

Yes and thanks for the clarification ajb.

 

No problem.

 

Commutative diagrams are the "bread and butter" of category theory. As such, they appear all over the place in mathematics. The idea is very simple. It does not matter which way you follow the arrows around.