cocontinuous
Adjective
Meaning
(mathematics, of a functor) Commutative with small colimits; right-exact and transforming small direct sums into small direct sums.
(organic chemistry) Blending two linear, amorphous polymers such that the phases interpenetrate.
Source: en.wiktionary.orgExamples
An important property of adjoint functors is that every right adjoint functor is continuous and every left adjoint functor is cocontinuous.
Dually, G is cocontinuous if and only if it preserves (small) coproducts and coequalizers.
Continuous and cocontinuous functors There are two natural types of functors between sites.
Since adjoint functors exist in abundance, this gives numerous examples of continuous and cocontinuous functors.