Ranges, restrictions, partial maps, and fibrations
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AbstractIn this thesis, we study range restriction categories and their properties. Range restriction categories with split restriction idempotents are shown to be equivalent to the partial map categories of ℳ-stable factorization systems. The notions of a restriction fibration, a range restriction fibration, a stable meet semilattice fibration, and a range stable meet semilattice fibration are introduced and it is shown that (range) stable meet semilattice fibrations provide a bridge between the category of (range) restriction categories and the category of categories and that (range) restriction fibrations are the same as (range) restriction categories so that these fibrations provide a useful setting for studying (range) restriction categories. Finally, we construct the free range restriction structures over directed graphs using deterministic trees.
Bibliography: p. 224-226