Injectivity in the Topos of Complete Heyting Algebra Valued Sets
Denis A. Higgs · Canadian Journal of Mathematics · 1984
Let be a complete Heyting algebra (CHA). An -valued set is a pair (X, δ) where X is a set and δ is a function from X × X to such that for all x, y z in X. -valued sets form a category as follows: a morphism from (X, δ) to (Y, δ) is a function f from X × Y to such that (i) f(x) ∧ δ(x, x′) ≦ f(x′, y), f(x, y) ∧ δ(y, y′) ≧ f(x, y′), (ii) f(x, y) ∧ f(x, y′) ≦ δ(y, y′), and (iii)