= Preservation obstructions to extending an adjoint chain
A <functor> admitting a further <left adjoint> must itself be a <right adjoint> and preserve all existing <categorical limits>. A functor admitting a further <right adjoint> must preserve all existing <colimits>. Failure to preserve a single <terminal object>, <equalizer>, <initial object> or <coproduct> therefore rules out the corresponding extension. In the <adjoint chain for the objects of a category>, connected components fail an equalizer and the <indiscrete category> functor fails a binary coproduct.
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