Add several negative properties of LRS_R deduced from those of Top

[dschepler]

Addresses: #227

[ScriptRaccoon]

Thanks a lot! I am glad that we can finally decide some of the properties of this category. It's also good to see that you could generalize your proof that previously only worked for special ground rings.

I have revised the content page, please check the three 3 commits that I added.

I still need to check the proofs in LRS_R.yaml. I will do this in the evening today.

[dschepler]

I have a question about the proof that Top does not have cartesian filtered colimits: the link given is proving that $\mathbb{Q} \times {-}$ does not preserve coequalizers, but coequalizers aren't filtered colimits. Is there some implication involved, not mentioned in the proof, that relates cartesian filtered colimits to "cartesian coequalizers"?

[ScriptRaccoon]

I have a question about the proof that Top does not have cartesian filtered colimits: the link given is proving that Q × − does not preserve coequalizers, but coequalizers aren't filtered colimits. Is there some implication involved, not mentioned in the proof, that relates cartesian filtered colimits to "cartesian coequalizers"?

The link is wrong, it should be https://math.stackexchange.com/questions/1255678 (it was correct once, at some point I made the wrong replacement).

The same link is used for Haus.

[ScriptRaccoon]

I have a question about the proof that Top does not have cartesian filtered colimits: the link given is proving that Q × − does not preserve coequalizers, but coequalizers aren't filtered colimits. Is there some implication involved, not mentioned in the proof, that relates cartesian filtered colimits to "cartesian coequalizers"?

The link is wrong, it should be https://math.stackexchange.com/questions/1255678 (it was correct once, at some point I made the wrong replacement).

Fixed in 275de99