I have to see that every left adjoint functor preserves initial objects.
I prove it by Adjoint functor theorem which states that under certain conditions a functor that preserves colimits is a left adjoint. A basic result of the category theory is that left adjoint preserves all colimits, which can be characterized as initial objects.
Is this idea correct to prove this statement "Every left adjoint funtor preserves initial objects"? or how can we see this.