Internal homotopy theory via classical completeness
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There is a wellestablished homotopy theory of simplicial objects in a Grothendieck topos, and folklore says that the weak equivalences are axiomatisable in the geometric fragment of L_{ω_1, ω}. It is in fact a theory of presheaf type, i.e. classified by a presheaf topos. Along the way, we will see how to apply classical completeness theorems to construct the homotopy theory of internal Kan complexes in any regular category.
This talk is part of the Category Theory Seminar series.
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