editing fonts of category links from the_category() funtion

If you are using the_category() (so without passing parameters), the result will be something like:

<ul class="post-categories">
<li><a href="https://wordpress.stackexchange.com/questions/262546/cat1">Category 1</a><li>
<li><a href="http://wordpress.stackexchange.com/cat2">Category 2</a><li>
</ul>

So a css line like .post-categories li a {font-family:Myfont;} should do it.

Reference: the_category() calls get_the_category_list, which does the actual output. This function ends with a filter, which you could use to assign further classes, even to individual links.