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Injectivity in the Topos of Complete Heyting Algebra Valued Sets

Published online by Cambridge University Press:  20 November 2018

Denis Higgs
Denis Higgs*
Affiliation:
University of Waterloo, Waterloo, Ontario
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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)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 3 , 01 June 1984 , pp. 550 - 568
Copyright
Copyright © Canadian Mathematical Society 1984

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