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Internal homotopy theory via classical completeness

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If you have a question about this talk, please contact Julia Goedecke .

There is a well-established homotopy theory of simplicial objects in a Grothendieck topos, and folklore says that the weak equivalences are axiomatisable in the geometric fragment of L_{Ī‰_1, Ī‰}. 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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Centre of African Studies and the Department of the History and Philosophy of Science Lecture Theatre 3, Judge Business School, Trumpington Street, Cambridge CB2 1AG Chetwynd Room, King's College, Cambridge

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