How to fetch Category of current Entry and build "Next / Prev" urls
A category is an element. So is an entry, and an asset, and a tag, and user. When you relate one element with another you get returned an ElementCriteriaModel in the template. So you need to use its methods to actually get the element data. In this case first().

So if you know for sure that you only have (and care about) one category in an entry, then you can try this for your params.

{% set params = craft.entries.section('projects').order('title asc').relatedTo(entry.category.first()) %}


You could also set category way up at the top of the template if you know you'll 
use it multiple times in the template. That way you are only making one database query.

{# At the top of the template #}
{% set category = entry.category.first() %}

{# Somewhat lower to display the category #}
{{ category.title }}

{# even lower to pull the other entries. #}
{% set params = craft.entries.section('projects').order('title asc').relatedTo(category) %}