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From: Gaucher Philippe <Philippe.Gaucher@pps.jussieu.fr>
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Subject: right adjoint by forgetting relational symbols
Date: Wed, 15 Oct 2008 12:03:23 +0200
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Dear all,

I need some references for this problem. Suppose we have a locally
presentable category C axiomatized by a limits theory T, so C=Mod(T).
Let us forget some relational symbols in T and all axioms containing these
relational symbols. One obtains a theory T'. There is a forgetful functor
Mod(T) --> Mod(T'). Does this functor have always a right adjoint ? If not,
what conditions must we add ?

Thanks in advance. pg.