The definition of toposes has surprisingly powerful consequences. (For example, toposes have all finite colimits.)

Probably the best analogy elsewhere in which a couple of mild-sounding hypotheses pick out a very narrow and interesting class of examples is the way in which the Cauchy-Riemann equations select the analytic functions from all smooth functions of a complex variable.

Michael Barr & Charles Wells, Toposes, Triples, and Theories (p 64)

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