[[Adjoint functor]]
# Right adjoint functors are continuous

Suppose we have an [[Adjoint functor|adjunction of functors]] $F \dashv U : \cat D \leftrightarrows \cat C$.
Then $U$ is a [[Continuity and cocontinuity|continuous functor]]
and $F$ is a [[Continuity and cocontinuity|cocontinuous functor]]. #m/thm/cat

> [!missing]- Proof
> #missing/proof

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