Timeline for Standard name of "atomic morphisms"?
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Jan 13, 2010 at 11:31 | vote | accept | Hans-Peter Stricker | ||
| Jan 4, 2010 at 16:06 | comment | added | t3suji | I agree that Mike's definition is more meaningful, but I would also consider an even stricter version. The problem is that even this definition is pretty much vacuous if the category has products or coproducts... (e.g., if there are products, any $f$ factors through $C=B\times A$, or in fact $C=B\times X$ for any $X$). So how about restricting the notion of atomic morphisms to monomorphisms (or dually, epimorphisms)? E.g.: A monomorphism $f$ is atomic if for any decomposition $f=g\circ h$ into a product of monomorphisms, either $g$ or $h$ is an isomorphism. | |
| Jan 4, 2010 at 16:01 | history | answered | Mike Shulman | CC BY-SA 2.5 |