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On model-comparison results for $\infty$-categories

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Speaker: 
Emily Riehl (Johns Hopkins)
Datum: 
Die, 19/01/2016 - 13:45 - 14:45
Location: 
MPIM Lecture Hall

The introduction of each new de finition of a weak higher
category poses an accompanying comparison problem, the challenge
being to convert between higher categories de fined via the
new model and higher categories de fined via pre-existing models.
A secondary question is whether proofs involving a particular model
of higher categories have any implications for other related models.
This talk will give a preliminary report on work in progress with
Dominic Verity that develops a framework in which categorical constructions
defi ned with one model of $(\infty, n)$-categories can be translated
into other models of (8,k)-categories. For the well-behaved
models of $(\infty,1)$-categories -- including quasi-categories, complete
Segal spaces, and Segal categories -- this work specializes to establish
the model independence of their basic category theory.

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