Linked spaces, originally motivated by applications to TQFTs, simultaneously simplify and generalise stratified spaces. I will briefly introduce the concept and the accompanying exit-path quasi-category construction. To exhibit the nontriviality of the generalisation, I will then consider some fundamental categories (as in "fundamental groupoid") of linked spaces and realise, from a "twist" of the complement of the trefoil knot with a point defect, a two-object category where the hom-set is the modular group PSL(2,Z) and argue that there is no stratified space with this fundamental category.