Geodesic
Pullbacks in Regular Categories
Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 251-255

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Given a pair of maps in a category, we would like to know whether they form part of a pullback diagram as follows: I am indebted to Basil Rattray for mentioning the solution of this problem for the category of sets. Here we shall solve it for any regular category in the sense of Barr [1].It will be useful to make the following definition. 
Meisen, Jeanne. Pullbacks in Regular Categories. Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 251-255. doi: 10.4153/CMB-1973-043-5
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     title = {Pullbacks in {Regular} {Categories}},
     journal = {Canadian mathematical bulletin},
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     doi = {10.4153/CMB-1973-043-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-043-5/}
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