Trace in additive categories
Published online by Cambridge University Press: 24 October 2008
Extract
1. Let ℳ be an additive category. (We refer to ((1), Ch. IX) for the definition of an additive category and associated terms. In particular a sequence
is exact if i = kerp and p = coker i.) We write End M for Hom(M, M). A trace on ℳ with values in an abelian group G is a collection of (abelian group) homomorphisms
one for each M ∈ ℳ, satisfying the following two conditions:
(i) Exactness. Given a commutative diagram with exact rows,
then tA(f) + tC(h) = tB(g).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 541 - 547
- Copyright
- Copyright © Cambridge Philosophical Society 1970
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