Vue named views with lazy loading - vue.js

Question

I am trying to create my routes, but I want them to all use the default router-view in my app.
Looking at the documentation:
https://router.vuejs.org/guide/essentials/named-views.html
I should be able to target views by doing something like this:
const routes = [
{
path: "/",
name: "home",
component: {
default: Home
},
},
]
I want to do this with a child, so I did this:
{
path: "/categories",
name: "categories",
meta: {
title: "Categories",
},
component: Categories,
children: [
{
path: ":slug",
name: "product-list",
meta: {
title: "Categories",
},
component: { default: ProductList },
],
},
],
},
I get no compile errors, but when navigating to /categories/televisions it only shows the Categories component, not the ProductList.
So my first question is, can children target app level router-view?
I also tried to add a new router-view like this:
<router-view />
<router-view name="root" />
and then updated my routes to this:
{
path: "/categories",
name: "categories",
meta: {
title: "Categories",
},
component: Categories,
children: [
{
path: ":slug",
name: "product-list",
meta: {
title: "Categories",
},
component: { root: ProductList },
},
],
},
But this didn't work either.
If it is possible to do this, then my next question, which is where I am heading.
Can I use lazy loaded components and target named/default router-views?
For example, I have this function:
const lazyLoad = (name) => {
return () => import(`../views/${name}/${name}.component.vue`);
};
Which I call from my routes like this:
{
path: "/categories",
name: "categories",
meta: {
title: "Categories",
},
component: lazyLoad("categories"),
children: [
{
path: ":slug",
name: "product-list",
meta: {
title: "Categories",
},
component: lazyLoad("product-list"),
},
],
},
Can I do it like this?
{
path: "/categories",
name: "categories",
meta: {
title: "Categories",
},
component: lazyLoad("categories"),
children: [
{
path: ":slug",
name: "product-list",
meta: {
title: "Categories",
},
component: { default: lazyLoad("product-list") },
},
],
},
and target the root router-view?