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:
“Although this garrulity of advising is born with us, I confess that life is rather a subject of wonder, than of didactics. So much fate, so much irresistible dictation from temperament and unknown inspiration enter into it, that we doubt we can say anything out of our own experience whereby to help each other.”
—Ralph Waldo Emerson (1803–1882)