How do I display current category slug in page

I am vaguely aware of programming and how it works (generally enough to get me in trouble). I am trying to have the category slug to actually appear on a page as text, and I can’t seem to find it in the supporting documentation. I just am not sure what the code is to have the name of the slug appear on a page post.

Basically I am using postlist plugin. I would like to use that plugin to display on the sidebar all posts that are involved with that category (by using a widget). I would like to do this dynamically by naming my postlists according to the slug of the category they refer too (which I have already done). All this leaves me is being able to display in text what the slug name for the current category selected in the text, it should dynamically switch the listed posts on the sidebar, depending on what the category is.

Unless someone knows a plugin that does this, which case I would be happy to be referred to it.