Using the definition given below, I wonder whether we can deduce that for each object A in C',(adsbygoogle = window.adsbygoogle || []).push({});

the identity for A in C' coincides with the identity for A in C.

Let C' and C be two categories which satisfies that

(i)each objects in C' belongs to C

(ii)each hom-set in C' is contained in the corresponding hom-set in C.

(iii)each composition in C' is the restriction of that in C .

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