## Fiat lax

### Alexander Campbell – 21 March 2018

Abstract: Gepner and Haugseng's definition of enriched infinity-category is an infinity-categorical analogue of Benabou's definition of an enriched category as a lax functor from a chaotic category to the suspension of a monoidal category. In this talk I will use two-dimensional monad theory to show that the strict analogue of the definition of lax functor used by Gepner and Haugseng (as a functor over Delta^op that preserves cocartesian lifts of inert morphisms) agrees with the standard definition of lax functor due to Benabou.

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