Timeline for "Infima" and "suprema" in the homomorphism preorder on hypergraphs on $\omega$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30 at 11:37 | comment | added | bof | @pastebee It seems that "categorical product" is another name for the direct product: en.wikipedia.org/wiki/Tensor_product_of_graphs. It's defined so that the projection maps are homomorphisms. | |
| Jan 30 at 9:54 | comment | added | paste bee | The category-theoretic product, which is described here, also has property 2. I don't know what the direct tensor product of two hypergraphs is, so I'm not sure if this is the same as bof's answer or not. These properties are direct consequences of the definitions of coproduct and product. | |
| Jan 30 at 9:50 | comment | added | bof | The disjoint union $H^*=H_1\sqcup H_2$ and the direct (tensor) product $H_*=H_1\times H_2$ have the desired properties. | |
| Jan 29 at 17:43 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
deleted 2 characters in body
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| Jan 29 at 9:27 | comment | added | Dominic van der Zypen | Right - I don't know whether this is known for graphs - not even for finite ones! I should have made the scope of the question much smaller. I will write a new question soon with the focus on graphs, possibly just finite ones. | |
| Jan 28 at 19:53 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |