Cohesion and the category of categories

Cohesion and the category of categories

[Venkata Rayudu Posina]

Dear All,

Since the structure of CATEGORY is of reflexive graph type and since
the category of reflexive graphs is cohesive, can we say that the
category of categories is cohesive.  I am not sure how the additional
structure i.e. composition that a category has on top of the reflexive
graph structure effects its cohesiveness.  I am thinking that somewhat
like reversible graphs, which have additional structure (action of
involution) besides the reflexive graph structure (action of two
idempotents) but nevertheless cohesive, the category of categories is
cohesive.  On the other hand, in going from actions of two idempotents
to actions of one idempotent, the cohesiveness of the category of
reflexive graphs changes into contrasting quality type of the category
of idempotents.  Is there a general statement about how cohesiveness
of a structure changes as one adds or removes component structures.

Thank you,
posina
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