
Axioms for Modelling Cubical Type Theory in a Topos
The homotopical approach to intensional type theory views proofs of equa...
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Universal Properties in Quantum Theory
We argue that notions in quantum theory should have universal properties...
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A Metalanguage for Guarded Iteration
Notions of guardedness serve to delineate admissible recursive definitio...
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A Semantics for Hybrid Iteration
The recently introduced notions of guarded traced (monoidal) category an...
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Effective Kan fibrations in simplicial sets
We introduce the notion of an effective Kan fibration, a new mathematica...
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Lambda Congruences and Extensionality
In this work we provide alternative formulations of the concepts of lamb...
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Equalizing Financial Impact in Supervised Learning
Notions of "fair classification" that have arisen in computer science ge...
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Uniform Elgot Iteration in Foundations
Category theory is famous for its innovative way of thinking of concepts by their descriptions, in particular by establishing universal properties. Concepts that can be characterized in a universal way receive a certain quality seal, which makes them easily transferable across application domains. The notion of partiality is however notoriously difficult to characterize in this way, although the importance of it is certain, especially for computer science where entire research areas, such as synthetic and axiomatic domain theory revolve around notions of partiality. More recently, this issue resurfaced in the context of (constructive) intensional type theory. Here, we provide a generic categorical iterationbased notion of partiality, which is arguably the most basic one. We show that the emerging free structures, which we dub uniformiteration algebras enjoy various desirable properties, in particular, yield an equational lifting monad. We then study the impact of classicality assumptions and choice principles on this monad, in particular, we establish a suitable categorial formulation of the axiom of countable choice entailing that the monad is an Elgot monad.
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