Functor

Continuity and cocontinuity

A functor 𝐹 :𝖢 →𝖣 is called continuous iff it commutes with (small) limits, i.e.

and cocontinuous iff it commutes with (small) colimits, i.e.

and bicontinuous iff it is both continuous and cocontinuous. #m/def/cat A weaker notion is Exact functor.

Results

• Right adjoint functors are continuous

#state/develop | #lang/en | #SemBr