Ok. First, read Understanding EE URLs.
Now, in your example - everything after index.php - there are several terms:
site/index/category/work/
site = {segment_1} = template group (not physical - in the database - Templates screen)
index = {segment_2} = template name (not physical - in the database - Templates screen)
category = {segment_3} = category URL indicator
work = {segment_4} = category url title
All of this is explained in the Semantics article on Displaying Categories, which I linked above.
Now, by default, the Category Heading tag, and the Weblog Entries tag will show entries only from the category in the URL. So you can use this one template to display *all of your categories* and the magic will restrict the entries shown by categories. So, for your code, all you’d need at a minimum - to show titles from both weblogs, in any given category is this:
{exp:weblog:entries weblog="articles|reports" limit="20" relaxed_categories="on"}
{title}
{/exp:weblog:entries}
Then simply visit it with the URL you gave above, change out Segment 4 with various category URL titles, you’ll note the entries listed change according to the category in the URL.
So go ahead, make a blank template, put the code here into it, and manually append the URLs. Actually, let me make it easier on you. Make a template in the site template group called learning_ee.
{!-- Explaining how the Category Heading Tag works --}
{exp:weblog:category_heading relaxed_categories="yes" weblog="articles|reports"}
<h1>{category_name}</h1>
{if category_description}
{category_description}
{/if}
{/exp:weblog:category_heading}
{!-- And the weblog entries tag --}
{exp:weblog:entries weblog="articles|reports" limit="20" relaxed_categories="yes"}
{title}: {categories}<a href="http://{path=">{category_name}</a>{/categories}
{/exp:weblog:entries}
{!-- And a path statement! --}
<a href="http://{path=">View full list, without category restriction</a>
Now, click “view rendered template”. Click on some categories, you’ll see the list of entries change based on category - all that in one template. =)
Edited to add some EE comments and the category heading tag.