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Uniform Kan fibrations from scratch

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It has been known for some time that the standard theory of Kan simplicial sets unavoidably uses non-constructive axioms. In recent work, Gambino and Sattler have made progress towards a constructive theory of Kan simplicial sets using algebraic weak factorization systems featuring ‘uniform’ Kan fibrations. In this talk I will show that it is possible to arrive at uniform Kan fibrations from scratch using a path object due to Garner and Van den Berg and a new class of generating trivial cofibrations called ‘mould inclusions’. This approach avoids non-constructive aspects of weak factorisation systems from the outset and focuses on Kan fibrations as modelling dependent types. This is joint work with Benno van den Berg.

This talk is part of the Category Theory Seminar series.

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