Elementary quotient completion

2012/06/01 by Maria Emilia Maietti, Maietti, Maria Emilia, Giuseppe Rosolini +1 · 4 citations
Computer Science · Mathematics · #03B15 #03B20 #03F55 #03G30 #18C50 #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.1206.0162

openalex publication_date 2012/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We extend the notion of exact completion on a weakly lex category to elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which freely adds effective quotients and extensional equality. We note that the elementary quotient completion can be obtained as the composite of two free constructions: one adds effective quotients, and the other forces extensionality of maps. We also prove that each construction preserves comprehensions.

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