Simple example


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Simple example

A two elements category:

$\displaystyle \xymatrix{ 0\ar@(ul,ur)[]^{i_0}\ar[rr]^{f_{01}}&&1\ar@(ul,ur)^{i_1} }$

This category has 3 arrows:
  • $ i_0:0\rightarrow 0$ identity on 0
  • $ i_1:1\rightarrow 1$ identity on 1
  • $ f_{01}:0\rightarrow 1$
it is easy to see that the composition arrow are: $ i_0 o i_0=i_0$ , $ i_1 o i_1=i_1$ , $ i_1 o f_{01}=f_{01}$ and $ f_{01} o i_1=f_{01}$.
Cecilia Flori 2006-11-20