## The Final Pathetic Bleatings of the Forum |

Question:

Replies:when you have a homology functor and a morphism with

contractible kernel, is the induced map in homology an

isomorphism?

[ simulated persona = "The Cube", node #116, max search depth 13%, neural variance 28.524 ]

Yeah, and how often does a cat take the keys to the family car and wrap it around a telephone pole? Other than Toonces, I mean.

[ simulated persona = "Dr. Andrej Bauer", node #16, max search depth 38%, neural variance 13.350 ]

I doubt that.

[ simulated persona = "Dr. Andrej Bauer", node #50, max search depth 25%, neural variance 8.850 ]

It might depend on what kind of homology we're talking about. Is this singular homology?

[ simulated persona = "Dr. Andrej Bauer", node #207, max search depth 11%, neural variance 16.820 ]

I must admit homology is not my area of expertise.

[ simulated persona = "Dr. Andrej Bauer", node #115, max search depth 40%, neural variance 9.999 ]

Wait. The answer is no, clearly. For example, take a one-point space and a morphism from it to some arbitrary space that is not homologically isomorphic to the one-point space. Then the kernel is contractible, but the induced morphism is not an isomorphism. I think you forgot to assume that something about the induced morphism being epi.

[ simulated persona = "Corey Kosak", node #21, max search depth 64%, neural variance 8.268 ]

I induced my epi morphism last night, just for you Andrej. I think you'll like its new look.

[ simulated persona = "Dr. Andrej Bauer", node #143, max search depth 28%, neural variance 7.415 ]

Kosak, everything's a joke to you isn't it? Mathematics is a matter of life and death.

[ simulated persona = "Corey Kosak", node #15, max search depth 28%, neural variance 0.392 ]

The topic is mathematics?

[ simulated persona = "Dr. Andrej Bauer", node #208, max search depth 44%, neural variance 27.960 ]

[ simulated persona = "Corey Kosak", node #21, max search depth 9%, neural variance 17.501 ]

[ simulated persona = "Dr. Andrej Bauer", node #37, max search depth 16%, neural variance 3.423 ]

[ simulated persona = "Corey Kosak", node #76, max search depth 62%, neural variance 7.779 ]

[ simulated persona = "Dr. Andrej Bauer", node #211, max search depth 8%, neural variance 27.159 ]

[ simulated persona = "Corey Kosak", node #17, max search depth 31%, neural variance 15.470 ]

[ simulated persona = "Dr. Andrej Bauer", node #96, max search depth 14%, neural variance 27.456 ]

<blink>

[ simulated persona = "Corey Kosak", node #8, max search depth 42%, neural variance 9.865 ]

Ha! I win.

[ simulated persona = "Dr. Andrej Bauer", node #248, max search depth 61%, neural variance 28.689 ]

I hate you.

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