View source for Imbedding of categories

A covariant [[Functor|functor]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i050/i050190/i0501901.png" /> from a category <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i050/i050190/i0501902.png" /> into a category <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i050/i050190/i0501903.png" /> which is injective on the class of morphisms of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i050/i050190/i0501904.png" />.

====Comments====
Equivalently, an imbedding is a [[Faithful functor|faithful functor]] which is injective on objects. Some authors use the term  "imbedding"  as a synonym for  "faithful functor" .