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full functor (Definition)

A functor $ T:\mathcal{C}\to\mathcal{D}$ is full if the arrow function of $ T$ is surjective for every pair of objects in $ \mathcal{C}$. More precisely, for every pair $ C_1, C_2\in \operatorname{Ob}(\mathcal{C})$, the arrow function $ T_{(C_1,C_2)}$ of $ T:$

$\displaystyle T_{(C_1,C_2)}:\operatorname{hom_{\mathcal{C}}}(C_1,C_2)\to\operatorname{hom_{\mathcal{D}}}(T(C_1),T(C_2))$
given by $ T_{(C_1,C_2)}(f)=T(f)$ is a surjection.



"full functor" is owned by CWoo.
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See Also: faithful functor
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Cross-references: surjection, objects, surjective, functor
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This is version 1 of full functor, born on 2004-05-11.
Object id is 5848, canonical name is FullFunctor.
Accessed 2246 times total.

Classification:
AMS MSC: 18A22 (Category theory; homological algebra :: General theory of categories and functors :: Special properties of functors )
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