Hello, I am taking as my concrete topos the category of irreflexive graphs.

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From William Lawvere's book (and many other sources), I know what the subobject classifier looks like, i.e. what graph is the subobject classifier. I haven't worked out the internal Heyting algebra Omega yet, but Hom[1, Omega] consists of three arrows, yes? (Sorry I know the question is a little basic, but I need a sanity check).

Thanks and regards, Bill Halchin