Accesing craft.categories.slug ids within a MatrixBlock for search query
I wanted to post this in case someone can use a portion of it to help with their search queries. This is what we came up with, works in combination with our three other category dropdowns (all four can be multiple selections), plus some custom Javascript. 

{% set categoriesArray = ['and'] %}

{# Institution #}
{% set searchInstitution = craft.request.getParam('institution') | replace({'|' : '\''}) %}
{% if searchInstitution is not empty %}
{% set institutions = craft.categories.search( searchInstitution ) %}
{% set categoriesArray = categoriesArray|merge([{targetElement: institutions, field: 'position.institution'}]) %}
{% endif %}


JS

var institutionNames = cbxInstitution.toArray()
      .reduce(function (p, c) {
        if (c.checked) p.push(c.value);
        return p;
      }, []);
    inInstitution.val(institutionNames.map(function(v){ return "|"+v.trim()+"|"; }).join(" OR "));