Timeline for Do coproducts in categories of algebras preserve monos?
Current License: CC BY-SA 2.5
4 events
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| Apr 4, 2011 at 12:05 | comment | added | Rob Myers |
The motivation comes from coalgebras for a finitary endofunctor T on a variety. T-coalgebras are algebra morphisms A --> TA, where elements of A have a 'behaviour' via a unique map to the final coalgebra. Coalgebras dualise algebras for a functor. It is somehow natural to consider FX + T-coalgebras for a fixed set X, since A --> FX + TA may be viewed as a T-coalgebra plus labels'. Such labels can be used to define operations over coalgebras, like a label one jumps to via a goto'. Coalgebra often assumes the functor preserves monos, so if T preserves monos, FX + T should also preserve them.
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| Apr 4, 2011 at 1:53 | comment | added | Todd Trimble | I was trying to subject my somewhat offhand guess to some more acidic tests today. Still no conclusion, but I was led to the category of relation algebras where a pushout of a pair of monos need not be a pair of monos (that is, the coprojections to the pushout need not be monic). Could you describe in your question what your motivations might be? Are they connected with mathematical logic? | |
| Apr 2, 2011 at 23:51 | comment | added | Rob Myers | Thanks a lot, that answers the title question. In fact it is the more specific question that I have been trying to prove, but have only succeeded in checking some specific cases e.g. distributive lattices, boolean algebras, modules over rings. | |
| Apr 2, 2011 at 23:01 | history | answered | Todd Trimble | CC BY-SA 2.5 |