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gregodom
gregodom
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Let $A$ and $B$ be two completecocomplete categories (i.e. closed under small colimits) and $A'$ be a dense subcategory of $B$$A$ i.e. any object in $A$ is a colimit of objects in $A'$. Given a functor $F': A' \to B$, does there always existsexist an extension of functor $F :A \to B$ preserving all colimits?

Let $A$ and $B$ be two complete categories (i.e. closed under small colimits) and $A'$ be a dense subcategory of $B$ i.e. any object in $A$ is a colimit of objects in $A'$. Given a functor $F': A' \to B$, does there always exists an extension of functor $F :A \to B$ preserving all colimits?

Let $A$ and $B$ be two cocomplete categories (i.e. closed under small colimits) and $A'$ be a dense subcategory of $A$ i.e. any object in $A$ is a colimit of objects in $A'$. Given a functor $F': A' \to B$, does there always exist an extension of functor $F :A \to B$ preserving all colimits?

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gregodom
gregodom
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extending functor from a dense subcategory

Let $A$ and $B$ be two complete categories (i.e. closed under small colimits) and $A'$ be a dense subcategory of $B$ i.e. any object in $A$ is a colimit of objects in $A'$. Given a functor $F': A' \to B$, does there always exists an extension of functor $F :A \to B$ preserving all colimits?