How to implement angular routing for product categories?

I’m creating a webshop in angular with firebase. I don’t want to create a different component for each category. Example route: /products/tables it should list out all the tables. 2nd example: /products/chairs it should list out all the chairs. When a user clicks on a chair the route should be: /products/chairs/1234 where 1234 is the product id. Is this possibble without defining every single category as a route?

app.routing.ts:

import { NgModule } from '@angular/core';
import { RouterModule, Routes } from '@angular/router';
import { CategoryComponent } from './products/category/category.component';
import { ProductComponent } from './products/category/product/product.component';
import { ProductsComponent } from './products/products.component';
const routes: Routes = [
    { path: '', pathMatch: 'full', component: ProductsComponent },
    { path: 'products/:category', component: CategoryComponent },
    { path: 'products/:category/:id', component: ProductComponent },
];
@NgModule({
    imports: [RouterModule.forRoot(routes)],
    exports: [RouterModule],
})
export class AppRoutingModule {}

app.component.html:

<router-outlet></router-outlet>

products.components.ts:

import { Component, OnInit } from '@angular/core';
import { ProductsService } from '../products.service';
@Component({
    selector: 'app-products',
    template: `
        <h1>Products:</h1>
        <ul>
            <li *ngFor="let category of categories">
                <a routerLink="{{ 'products/' + category }}">
                    <h1>
                        {{ category }}
                    </h1>
                </a>
            </li>
        </ul>
    `,
    styleUrls: ['./products.component.css'],
})
export class ProductsComponent implements OnInit {
    categories: string[] = [];
    constructor(private productsService: ProductsService) {}
    ngOnInit(): void {
        this.categories = this.productsService.getCategoryNames();
    }
}

category.component.ts:

import { Component, OnInit } from '@angular/core';
import { ActivatedRoute, Params } from '@angular/router';
import { ProductsService } from 'src/app/products.service';
@Component({
    selector: 'app-category',
    template: `
        <h1>Products in {{ category }} category:</h1>
        <ul>
            <li *ngFor="let product of products; index as i">
                <a routerLink="{{ i }}">
                    <h2>
                        {{ product }}
                    </h2>
                </a>
            </li>
        </ul>
    `,
    styleUrls: ['./category.component.css'],
})
export class CategoryComponent implements OnInit {
    products: string[] = [];
    category = '';
    constructor(
        private route: ActivatedRoute,
        private productsService: ProductsService
    ) {}
    ngOnInit(): void {
        this.route.params.subscribe((params: Params) => {
            this.category = params['category'];
            this.products = this.productsService.getCategoryItems(
                this.category
            );
        });
    }
}

product.component.ts:

import { Component, OnInit } from '@angular/core';
import { ActivatedRoute, Params } from '@angular/router';
import { ProductsService } from 'src/app/products.service';
@Component({
    selector: 'app-product',
    template: `
        <h3>
            {{ product }}
        </h3>
    `,
    styleUrls: ['./product.component.css'],
})
export class ProductComponent implements OnInit {
    product = '';
    constructor(
        private route: ActivatedRoute,
        private productsService: ProductsService
    ) {}
    ngOnInit(): void {
        this.route.params.subscribe((params: Params) => {
            const category: string = params['category'];
            const id: number = params['id'];
            this.product = this.productsService.getProduct(category, id);
        });
    }
}

app.module.ts:

import { NgModule } from '@angular/core';
import { BrowserModule } from '@angular/platform-browser';

import { AppRoutingModule } from './app-routing.module';
import { AppComponent } from './app.component';
import { ProductsService } from './products.service';
import { CategoryComponent } from './products/category/category.component';
import { ProductComponent } from './products/category/product/product.component';
import { ProductsComponent } from './products/products.component';
@NgModule({
    declarations: [
        AppComponent,
        ProductsComponent,
        CategoryComponent,
        ProductComponent,
    ],
    imports: [BrowserModule, AppRoutingModule],
    providers: [ProductsService],
    bootstrap: [AppComponent],
})
export class AppModule {}

products.service.ts:

export class ProductsService {
    products: any = {
        tables: ['table1', 'table2', 'table3'],
        chairs: ['chair1', 'chair2', 'chair3', 'chair4'],
    };
    getProduct(category: string, id: number) {
        return this.products[category][id];
    }
    getCategoryItems(category: string) {
        return this.products[category];
    }
    getCategoryNames() {
        return Object.keys(this.products);
    }
}