Elementary quotient completion

By Maria Emilia Maietti, Giuseppe Rosolini. Theory and Applications of Categories, 2012

74 citations recorded by the source corpus.

We extend the notion of exact completion on a category with weak nite limits to Lawvere's elementary doctrines. We show how any such doctrine admits an ele- mentary quotient completion, which is the universal solution to adding certain quotients. We note that the elementary quotient completion can be obtained as the composite of two other universal constructions: one adds eective quotients, the other forces exten- sionality of morphisms. We also prove that each construction preserves comprehension.

Subfields: Artificial Intelligence, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/151db4d5de84142ccd7fc555ce57adc71e12e3f9