Citations:underlying functor

• 2007, Franz Baader, Term Rewriting and Applications: 18th International Conference, RTA 2007, Paris, France, June 26-28, 2007, Proceedings, Springer (Template:ISBN), page 127:

  The marked graphs and their homomorphisms form the category of marked graphs ${𝐆𝐫}^{\prime }$. Let $\mathrm{\Delta }:{𝐆𝐫}^{\prime }\to 𝐆𝐫$ denote the underlying functor, that forgets about the marking, and let $\mathrm{\nabla }:𝐆𝐫\to 𝐆{𝐫}^{\prime }$ 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 (Template:ISBN), page 64:

  In the example above we have seen that the free functor $F:𝔊\to {𝔐}_A$ is left adjoint to the underlying functor $G:{𝔐}_A\to 𝔊$. 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.