University of Birmingham > Talks@bham > Lab Lunch > Using Yoneda rather than J to present the identity type.

Using Yoneda rather than J to present the identity type.

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If you have a question about this talk, please contact Dr Steve Vickers.

I will explain that the induction principle J for Martin-Lof’s identity types amounts to the Yoneda Lemma, when types are seen as infty-groupoids (and hence categories). This holds internally in MLTT : from J we derive the Yoneda Lemma, and conversely from the Yoneda Lemma we derive J. Moreover, the computation rule for Yoneda gives the computation rule for J, and vice versa.

This talk is part of the Lab Lunch series.

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