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from the object to itself. This is the case here. For example, in the category of non-empty sets, the objects are sets and the arrows are mappings from a set to another (or to the same) set. This has to not be confused with the category that can be associated to a specific monoid, which has only one
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The formal definition of a category implies the existence of an identity arrow for each object. Because semi-groups do not have an identity element, I guess we should not call them "category of semigroups". Shall we not call them "questionable category of semigroups" or something in that spirit?
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object and whose arrows are the elements of the monoid. Contrarily to preceding examples the category associated to a monoid has only one identity element, while the category of sets (or of monoids) has many identity arrows (one for each set or monoid).
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The figure seems to show an object {0} that is terminal, but not initial (no arrows from {0} to any of the other elements of A).
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In the case of categories whose objects are sets or which have an underlying set, the identity arrow is the
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Shall we not avoid to talk about "Category of semi-groups" or "Category of non-empty Sets"
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