I had originally asked this question on Math StackExchange but have not obtained any answers, so I decided to post this here. (I have flagged the MSE post to be moved to MathOverflow, for the administrators.)
This question is in similar spirit to this question, but
I'm asking for references that meet all or one of the following criteria:
a general formulation of the theory of TQFTs from the mathematics perspective that also explains the significance of the results in physics, and
pure mathematical applications of TQFTs defined using categories.
I know about Urs Schreiber et. al's and Lurie's paper, but are there others?
Note that by "TQFT" I mean ordinary TQFTs and/or extended TQFTs. Also, as I don't have university access, I'd appreciate it if the references were available online in some form.