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Thanks for your attention,

I'm an undergraduate. I'm reading the book of Dieter Happel, Triangulated categories in the representation theory of finite dimensional algebras, I cannot prove this sentence:

"The maps factoring through an injective object are precisely the null-homotopic maps."

Here, the object is in the complex category.

Please give a complete proof or some references which take it!

  • 1
    You should describe the context in which that statement appears.2010-12-20
  • 2
    In any case, this follows from the very special form which the injective objects have: to see this, notice that you can describe precisely the indecomposable injectives.2010-12-20

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