Category Theory CMD

$ newset s0 -i 0 1 2 3 4
Created set `s0'
$ newset s1 -i 1 2 3 4 5
Created set `s1'
$ newset s2 -i 2 3 4 5 6
Created set `s2'
$ newset s3 -i 3 4 5 6 7
Created set `s3'
$
$ defn succ n -> n+1
Function `succ' created
$ defn pred n -> n-1
Function `pred' created
$
$ newcat $c --obt=Set --compose=FComp
Null category `c' created with `set' objects
$
$ cataddobs $c $s0 $s1 $s2 $s3
Added objects to category `c'
$ cataddmorph $c $s0 -> $s1 -m=$succ --name="f"
Added morphism to category `c'
$ cataddmorph $c $s1 -> $s2 -m=$succ --name="g"
Added morphism to category `c'
$ cataddmorph $c $s2 -> $s3 -m=$succ --name="h"
Added morphism to category `c'
$
$ cataddmorph $c $s3 -> $s2 -m=$pred --name="h'"
Added morphism to category `c'
$ cataddmorph $c $s2 -> $s1 -m=$pred --name="g'"
Added morphism to category `c'
$ cataddmorph $c $s1 -> $s0 -m=$pred --name="h'"
Added morphism to category `c'
$
$ catlistmorphs $c
* Morphisms:
id_s0 : s0 -> s0
id_s1 : s1 -> s1
id_s2 : s2 -> s2
id_s3 : s3 -> s3
f     : s0 -> s1
f'    : s1 -> s0
f . g : s0 -> s2
f.g.h : s0 -> s3
g     : s1 -> s2
g'    : s2 -> s1
g . h : s1 -> s3
h     : s2 -> s3
h'    : s3 -> s2
* Equivalences:
f . f' = id_s0
g . g' = id_s1
h . h' = id_s2