The category of topological spaces Top has objects the topological spaces and morphisms the continuous maps between them. The older definition of the homotopy category hTop, called the naive homotopy category for clarity in this article, has the same objects, and a morphism is a homotopy class of continuous maps. That is, two continuous maps "f": "X" → "Y" are considered the same in the naive homotopy category if one can be continuously deformed to the other. There is a functor from Top to hTop that sends spaces to themselves and morphisms to their homotopy classes. A map "f": "X" → "Y" is called a homotopy equivalence if it becomes an isomorphism in the naive homotopy category.