I’m trying to understand the concept of colimits for commutative rings, but unable to find a colimit(or at least a compliment) for a finite diagram of rings, is there a(non trivial) example for a compliment(and a colimit as a universal compliment) for a 2-3 rings diagram?
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What's a "compliment" in this context? – Thorgott Feb 15 '24 at 15:05
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For a diagram of rings and morphisms D, a compliment is defined as a ring A with a morphism from any ring J in D to A such that the diagram commutes – Roye sharifie Feb 15 '24 at 16:32
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That would usually be called a cocone. Have you tried starting with thinking about coproducts? See e.g. here. – Thorgott Feb 15 '24 at 17:38
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You could consider $\mathbb Z[1/m]\subset\mathbb Z[1/mn]\subset\cdots$ for positive (coprime) integers $m,n,\ldots$, all seen as subrings of $\mathbb Q$. – Andrew Hubery Feb 15 '24 at 20:10