Forgetful functors are a generalization of the canonical morphisms over algebraic structures. Given a group/ring/field/topological space $$A$$ and normal subgroup/ideal/sub-field/compact subset $$B$$, we can define the forgetful map $$A\to A\:/\:B$$by mapping every element to its representative in the quotient. In some sense, this map "ignores" some of the structure of $$A$$ in this map, reducing $$A$$ to a "simpler" structure.