Hello @DavidTanzer,

Below are few diagraph representation. I have dropped an incoming arrow to terminal object.

Does below graph indicate a generalized element

digraph G {

subgraph clusterA {1}

subgraph clusterC {x}

subgraph clusterD {y}

subgraph clusterB {a b c}

1 -> a -> 1

x -> b -> x

y -> c -> y

1 -> x -> 1

x -> y -> x

1 -> y -> 1

a -> x

a -> y

b -> 1

b -> y

c -> 1

c -> x

}

So there are three terminal object viz; 1, x and y. Since if there are more than one terminal object they are isomorphic in nature. Also, one terminal object probe one object from other category, so "1" probe "a" and "x" probe "b" and "y" probe "c".

So each object a, b and c terminates at each terminal object; 1, x and y

If this is true, there aren't the morphism from 1-> a and a-> isomorphic in nature?

Second, graph

digraph G {

subgraph clusterA {1}

subgraph clusterB {a b c}

1 -> a -> 1

1 -> b -> 1

1 -> c -> 1

}

It's a similar to first one but with single terminal object. Again isn't this generalized element having an isomorphism with each object in other category

Below are few diagraph representation. I have dropped an incoming arrow to terminal object.

Does below graph indicate a generalized element

digraph G {

subgraph clusterA {1}

subgraph clusterC {x}

subgraph clusterD {y}

subgraph clusterB {a b c}

1 -> a -> 1

x -> b -> x

y -> c -> y

1 -> x -> 1

x -> y -> x

1 -> y -> 1

a -> x

a -> y

b -> 1

b -> y

c -> 1

c -> x

}

So there are three terminal object viz; 1, x and y. Since if there are more than one terminal object they are isomorphic in nature. Also, one terminal object probe one object from other category, so "1" probe "a" and "x" probe "b" and "y" probe "c".

So each object a, b and c terminates at each terminal object; 1, x and y

If this is true, there aren't the morphism from 1-> a and a-> isomorphic in nature?

Second, graph

digraph G {

subgraph clusterA {1}

subgraph clusterB {a b c}

1 -> a -> 1

1 -> b -> 1

1 -> c -> 1

}

It's a similar to first one but with single terminal object. Again isn't this generalized element having an isomorphism with each object in other category