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We will work with small catetories, especially those catetories with a finte \
set of generators and relations.\
\>", "Text",
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We denote by hom[X, Y]  the set of arrows whose domain is X and whose \
codomain is Y. \
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The composition rules may be given as a function that takes a pair of arrows \
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category.
In ex. 4, we have only one object. So, we have only to work with
hom[A,A]\[Times]hom[A,A]\[RightArrow]hom[A,A].\
\>", "Text",
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The data structure for the composition rule may be given as follows.\
\>", "Text",
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Cell["\<\
hom[A, B]\[Times]hom[B, C]\[Times]hom[C, D]\[RightArrow]hom[A,D]   can be \
constructed in two ways:
(hom[A, B]\[Times]hom[B, C])\[Times]hom[C, D]\[RightArrow]hom[A,D]   and
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Without the HoldAll attribute, we would get no meaningful results. You may try
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In this example, we have two objects A and B and an arrow \[Alpha] besides \
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