We have translated Bénabou’s “équivalence nucléaire” as “kernel pair”. We have translated Bénabou’s “noyau du couple” as “equalizer” — a usage of the French school that is explained by Grothendieck in his 1965-1966 lectures on basic category theory (Introduction Au Langage Fonctoriel, 1966, I.6.3.2). I have also renamed some of the labels in the first commutative diagram of Definition 2.1 [000B] for clarity.