Abstract
Let A be an abelian category with enough projectives and let ℋ be the quotient category of A obtained by identifying with zero all maps which factor through projectives. ℋ is the Eckmann-Hilton homotopy category.) Do idempotents split in ℋ? That is, given \( A\,\xrightarrow{e}\,A\, \in \,\mathcal{H} \), e2 ≡ e does there exist B ∈ ℋ and maps A → B, B → A such that A → B → A ≡ e, B → A → B ≡1?
Received September 5, 1965.
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© 1966 Springer-Verlag Berlin · Heidelberg
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Freyd, P. (1966). Splitting Homotopy Idempotents. In: Eilenberg, S., Harrison, D.K., MacLane, S., Röhrl, H. (eds) Proceedings of the Conference on Categorical Algebra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-99902-4_6
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DOI: https://doi.org/10.1007/978-3-642-99902-4_6
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