Hi, everyone:(adsbygoogle = window.adsbygoogle || []).push({});

I keep seeing, mostly in homological algebra, the use of "induced

homomorphs" or "induced isomorphisms". I get the idea of what is

going on, but I have not been able to find a formal result that

rigorously explains this, i.e, under what conditions does a map

induce an isomorphism or a homomorphism?. The only patterns

there seems to be in all these induced maps is that they are all

defined in some quotient space of the domain, i.e, if

we have f:X->Y , then the induced maps f* are , or seem to be,

defined in X/~ , for some equiv. relation ~ (e.g, in homotopy and

homology). Also, maybe obviously, f is a continuous map.

Basically: I would like to know a result that would allow me to

give a yes/no answer to the question : does f:X->Y induce an

isomorphism/homomorphism of some sort?

Thanks.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Induced Homomorphs, Isomorphs.

Loading...

Similar Threads - Induced Homomorphs Isomorphs | Date |
---|---|

I Division Rings & Ring Homomorphisms ... A&W Corollary 2.4 .. | Tuesday at 3:51 AM |

Question about induced matrix norm | Jan 23, 2016 |

Types of Induced Maps. | May 25, 2014 |

Norm induced by inner product? | Apr 4, 2012 |

Definition of induced representation | Sep 30, 2011 |

**Physics Forums - The Fusion of Science and Community**