Collocations for mat - noun

rubber, straw, woven
judo, wrestling, yoga, etc.
prayer, sleeping
bath
mouse (BrE) (mouse pad in AmE)
Every computer user should have a good mouse mat.

beer (BrE)
dense, thick
a thick mat of hair

lay, lay out, roll out, unroll
The man unrolled his prayer mat.

mat of
the dense mat of roots at the bottom of the tree

put out the welcome mat, roll out the welcome mat (both figurative, esp. AmE)
They hoped the country would put out a welcome mat for Western investment.