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:
“For a painter, the Mecca of the world, for study, for inspiration and for living is here on this star called Paris. Just look at it, no wonder so many artists have come here and called it home. Brother, if you can’t paint in Paris, you’d better give up and marry the boss’s daughter.”
—Alan Jay Lerner (1918–1986)