Is there a notion of 'objective' in Hegelian Theory?

Question

According to the wikipedia entry on Categorical Logic:

Lawvere's writings, sometimes couched in a philosophical jargon, isolated some of the basic concepts as adjoint functors (which he explained as 'objective' in a Hegelian sense, not without some justification).

Hegel had continued with Kants bridging of the world of the subject & object, but whereas Kant mentions antinomies only in passing to point out the limits of experience, Hegel makes this the engine that drives his philosophy through his triadic dialectic.

Lawvere is known for advocating the adjunction between the space of logics and the space of its concrete models. Possibly he considered this a motion between the world of thought and that of concrete reality. But there is no sense of a dialectic here in the Hegelian sense.

Is there a well-known way that Hegel used the term 'objective'? For example, I've come across 'Objective Spirit'.

Answer 1

Hegel, in the third part of his Encyclopedia of the Philosophical Sciences, titled the Philosophy of Spirit, he identifies a tripartite division of spirit - into subjective, objective & absolute spirit.

According to the SEP, his objective spirit is the form in which spirit is objectified into social interactions & social institutions.

Its possible that Lawvere (loosely) identifies how an adjunction reifies the relationship between an abstract logic with its objective form, with how the objective spirit reifies spirit into the objective forms of sociality in its manifold forms.