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1. • CommentRowNumber1.
   • CommentAuthorAndrew Stacey
   • CommentTimeJul 25th 2011
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   Author: Andrew Stacey
   Format: MarkdownItexI thought that this was _dense_, but looking at the page [[dense functor]] then I'm wrong. To be clear, I have a functor $F \colon C \to D$ with the property that every object in $D$ is isomorphic to one in the image of $C$. In my case, $F$ happens also to be an inclusion of a subcategory. What's the name for this?

   I thought that this was dense, but looking at the page dense functor then I’m wrong.

   To be clear, I have a functor $F \colon C \to D$ with the property that every object in $D$ is isomorphic to one in the image of $C$. In my case, $F$ happens also to be an inclusion of a subcategory. What’s the name for this?

2. • CommentRowNumber2.
   • CommentAuthorYaron
   • CommentTimeJul 25th 2011
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   Author: Yaron
   Format: MarkdownItexI think that the first property makes your functor an [[essentially surjective functor]] (and the second makes it faithful).

   I think that the first property makes your functor an essentially surjective functor (and the second makes it faithful).

3. • CommentRowNumber3.
   • CommentAuthorAndrew Stacey
   • CommentTimeJul 25th 2011
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   Author: Andrew Stacey
   Format: MarkdownItexThat looks right! Thanks.

   That looks right! Thanks.

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeJul 25th 2011
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   Author: TobyBartels
   Format: MarkdownItexSo "essentially surjective subcategory"?

   So “essentially surjective subcategory”?

5. • CommentRowNumber5.
   • CommentAuthorAndrew Stacey
   • CommentTimeJul 25th 2011
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   Author: Andrew Stacey
   Format: MarkdownItexThat sounds a bit yucky, but fortunately I have the functor explicitly so I can say "essentially surjective functor".

   That sounds a bit yucky, but fortunately I have the functor explicitly so I can say “essentially surjective functor”.

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeJul 27th 2011
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   Author: Mike Shulman
   Format: MarkdownItexHow about [[essentially wide subcategory]]?

   How about essentially wide subcategory?

7. • CommentRowNumber7.
   • CommentAuthorAndrew Stacey
   • CommentTimeJul 27th 2011
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   Author: Andrew Stacey
   Format: MarkdownItexLooks good to me! Thanks. So we have [[essentially surjective functor]] for the functor, and [[essentially wide subcategory]] for the subcategory. Great.

   Looks good to me! Thanks. So we have essentially surjective functor for the functor, and essentially wide subcategory for the subcategory. Great.

8. • CommentRowNumber8.
   • CommentAuthorTobyBartels
   • CommentTimeJul 27th 2011
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   Author: TobyBartels
   Format: MarkdownItexI added the terminology for the subcategory for the page on the functor (the reverse was already there).

   I added the terminology for the subcategory for the page on the functor (the reverse was already there).