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Difference between revisions of "Imbedding of categories"

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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" />.
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A covariant [[Functor|functor]] $F$ from a category $C$ into a category $C_1$ which is injective on the class of morphisms of $C$.
  
 
====Comments====
 
====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" .
 
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" .

Latest revision as of 14:16, 17 July 2014

A covariant functor $F$ from a category $C$ into a category $C_1$ which is injective on the class of morphisms of $C$.

Comments

Equivalently, an imbedding is a faithful functor which is injective on objects. Some authors use the term "imbedding" as a synonym for "faithful functor" .

How to Cite This Entry:
Imbedding of categories. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Imbedding_of_categories&oldid=32460
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