I found (a rather trivial) counter-example to one conjecture I considered in the past:
Example for some convex reloid .
Proof Let . Then . Let is some nontrivial atomic filter object. Then and thus .
Before I found the last counter-example, I was thinking that is an isomorphism from the set of of funcoids to the set of convex reloids. As this conjecture failed, we need an other way to characterize the set of reloids isomorphic to funcoids.
The first thing we need to check is whether is an injection. Maybe this is a simple problem (or maybe it is hard) but I haven’t thought about it yet.