subcategory

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The functor H being the inclusion functor, we omit it from writing to simplify notation.
where Mon is just the inclusion functor from Gp to Mon.
When C is a regular strongly unital category with finite colimits, the inclusion functor AbC [right arrow] C from the full subcategory of abelian objects in C admits a left adjoint which is given by the cokernel of the diagonal [s.