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January 15, 2025

The Dual Concept of Injection

Posted by Tom Leinster

We’re brought up to say that the dual concept of injection is surjection, and of course there’s a perfectly good reason for this. The monics in the category of sets are the injections, the epics are the surjections, and monics and epics are dual concepts in the usual categorical sense.

But there’s another way of looking at things, which gives a different answer to the question “what is the dual concept of injection?”

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