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We present a generative model enhancing external categories through novel axioms in topology.
We present a structural extension to the generative framework of external categories established via faithful filters. By transitioning from a classical, Boolean valuation to a Heyting algebra-valued lattice Omega, we resolve the problem of local topological continuous categoricity. We introduce an upgraded set of axioms governing identity restriction and composition closure under structural meets , and solve the completeness/bijectivity problem for Omega-enriched sheaves using a local supremum selection rule.
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Omar M'NARI (2026) studied this question.
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