On setoids:
Olov Wilander, Constructing a small category of setoids, Mathematical Structures in Computer Science 22 1 (2012) 103-121 [doi:10.1017/S0960129511000478, pdf]
Erik Palmgren, Olov Wilander, Constructing categories and setoids of setoids in type theory, Logical Methods in Computer Science, 10 3 (2014) lmcs:964 [arXiv:1408.1364, doi:10.2168/LMCS-10(3:25)2014]
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