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Regular, exact, and PERs categories

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If you have a question about this talk, please contact Sean Moss .

There are different ways of dealing with equivalence relations and quotients. Notably:
  • Regular and exact categories: they arise naturally with many examples. Thus, their free constructions are of particular interest.
  • Categories of partial equivalence relations (PERs): they are widely used in computer science (particularly in semantics of programming languages). These notions are linked together and fall within a general framework. This provides an explanation of why all these categories are often found to be cartesian closed.
References:
  • Carboni, Celia Magno – The free exact category on a left exact one
  • Carboni, Vitale – Regular and exact completions
  • Carboni, Rosolini – Locally cartesian closed exact completions
  • Birkedal, Carboni, Rosolini, Scott – Type theory via exact categories

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