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Epimorphisms and Acyclic Types in Univalent Foundations

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arxiv 2401.14106 v3 pith:ZH6LRLFG submitted 2024-01-25 cs.LO math.ATmath.CT

Ulrik Buchholtz , Tom de Jong , Egbert Rijke This is my paper · ORCID
classification cs.LOmath.ATmath.CT
keywords acyclictheorytypesepimorphismsfoundationsgrouphomotopymaps
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We characterize the epimorphisms in homotopy type theory (HoTT) as the fiberwise acyclic maps and develop a type-theoretic treatment of acyclic maps and types in the context of synthetic homotopy theory as developed in univalent foundations. We present examples and applications in group theory, such as the acyclicity of the Higman group, through the identification of groups with 0-connected, pointed 1-types. Many of our results are formalized as part of the agda-unimath library.

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