Topological Inspiration
This complex is called the cone in analogy to the mapping cone (topology) of a continuous map of topological spaces : the complex of singular chains of the topological cone is homotopy equivalent to the cone (in the chain-complex-sense) of the induced map of singular chains of X to Y. The mapping cylinder of a map of complexes is similarly related to the mapping cylinder of continuous maps.
Read more about this topic: Mapping Cone (homological Algebra)
Famous quotes containing the word inspiration:
“Shakespeare carries us to such a lofty strain of intelligent activity, as to suggest a wealth which beggars his own; and we then feel that the splendid works which he has created, and which in other hours we extol as a sort of self-existent poetry, take no stronger hold of real nature than the shadow of a passing traveller on the rock. The inspiration which uttered itself in Hamlet and Lear could utter things as good from day to day, for ever.”
—Ralph Waldo Emerson (1803–1882)