Homotopy Coherent Adjunctions of Quasi-categories
نویسنده
چکیده
We show that an adjoint functor between quasi-categories may be extended to a simplicially enriched functor whose domain is an explicitly presented “homotopy coherent adjunction”. This enriched functor encapsulates both the coherent monad and the coherent comonad generated by the adjunction. Furthermore, because its domain is cofibrant, this data can be used to construct explicit quasi-categories of (co)algebras. Given time, we describe how our techniques can also be used to re-prove many of the foundational results about the category theory of quasi-categories. This is joint work with Dominic Verity.
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