Citations:underlying functor


 * 2007, Franz Baader, Term Rewriting and Applications: 18th International Conference, RTA 2007, Paris, France, June 26-28, 2007, Proceedings, Springer (ISBN 9783540734499), page 127:
 * The marked graphs and their homomorphisms form the category of marked graphs $$\mathbf{Gr}'$$. Let $$\Delta : \mathbf{Gr}' \rightarrow \mathbf{Gr}$$ denote the underlying functor, that forgets about the marking, and let $$\nabla : \mathbf{Gr} \rightarrow \mathbf{Gr'}$$ denote the functor that generates a marked graph  from a graph, by marking all of its reachable nodes.
 * 2012, Peter J. Hilton, Urs Stammbach, A Course in Homological Algebra, Springer Science & Business Media (ISBN 9781441985668), page 64:
 * In the example above we have seen that the free functor $$F: \mathfrak{G} \rightarrow \mathfrak{M}_A$$ is left adjoint to the underlying functor $$G: \mathfrak{M}_A \rightarrow \mathfrak{G}$$. The reader will readily verify that  the concept of a free group (free object in the category of groups) and the concept of a polynomial algebra over a field K (free object in the category of commutative K-algebras) may also be formulated in terms of a free functor left adjoint to an underlying functor.