nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqky223zcc4q69d8t0me4vg5uw8mw0yxeukjgvz6h92laqnenr0ajs7297ud (nprofile…97ud) I think there is some care that needs to be taken when upgrading the "removing element of a set" story to "removing an object of a category" one.
For instance, if there was another object `q` isomorphic to `p0` we removed, we'd end up with an equivalent category. So you likely want to remove the entire isomorphism class, but then I believe you run into further problems.
This thesis on Symmetric Containers (Section 2.3) goes into some detail: https://staff.math.su.se/gylterud/thesis_gylterud.pdf