I am not sure about the earliest references, but the standard ("non-tricky") facts are: 1. A x_B C ---> A x C is a regular mono, namely the equalizer of the two obvious morphisms A x C ---> B. 2. Every regular mono is extremal. George ----- Original Message ----- From: "Michael Barr" <barr@math.mcgill.ca> To: "Categories list" <categories@mta.ca> Sent: Monday, October 19, 2009 5:15 PM Subject: categories: pullback into product
If A ---> B <--- C is a pair of maps with the same codomain, then, assuming pullback and product both exist, the map A x_B C ---> A x C is an extremal monic. It is slightly tricky to prove, but must be well known. Can anyone give me a reference?
Michael
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