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Jan 21, 2014 at 15:02 comment added Ronnie Brown @Todd: I mention that the groupoid example of the integers was in essence in my 1967 paper on van Kampen's theorem and was in the 1968 book on Topology.
Jan 20, 2014 at 18:00 comment added Ronnie Brown @Todd: That example is a good one, and can also be phrased as a pushout in the category $Cat$ of small categories, noting that $Cat \to Sets$ is a bifibration of categories. Thanks also for the references.
Jan 18, 2014 at 21:53 comment added Todd Trimble I was thinking about this example too, except mine was the coequalizer in $\mathbf{Cat}$ of the two object inclusions of the terminal category $\mathbf{1}$ into the arrow category $\mathbf{2}$. The coequalizer is the monoid of natural numbers made into a 1-object category. This example appears in Lawvere's Category of Categories paper, and in Mathematics Made Difficult.
S Jan 18, 2014 at 15:32 history answered Ronnie Brown CC BY-SA 3.0
S Jan 18, 2014 at 15:32 history made wiki Post Made Community Wiki by Ronnie Brown