Vuejs <router-link> same route but different parameter

I want to filter product-list by [ men / women / all ] category, using the same ProductList.vue, but it doesn't refresh.

// headerPart.vue
                        <nav class="main-nav">
                            <router-link class="route" to="/cate/men">Men</router-link>
                            <router-link class="route" to="/cate/women">Women</router-link>
                            <router-link class="route" to="/cate/all">All</router-link>
                        </nav>

Solutions:

// App.vue
        <router-view :key="$route.path"></router-view>

stackoverflow.com/questions/56131100/vuejs-..

stackoverflow.com/questions/42603583/vue-js..

dev.to/erefor/vue-tip-same-component-differ..

snapshot by branch: github.com/sunpochin/vue2-ecommerce/tree/ge..