论文标题
伴随函数定理，用于同型富集类别
Adjoint functor theorems for homotopically enriched categories
论文作者
论文摘要
我们在富含单型模型类别的类别的设置中证明了一个伴随函数定理$ \ MATHCAL V $承认某些限制。当$ \ Mathcal V $配备琐碎的模型结构时，这将重新获得Freyd的伴随函数定理的丰富版本。对于非平凡的模型结构，我们获得了同质风味的新伴随函数定理 - 尤其是当$ \ Mathcal v $是简单组合的类别时，我们获得了适合$ \ infty $ \ infty $ \ iffty $ -Cosmoi的Riehl和Verity和Verity和Verity的同型伴随函数定理。我们还调查了在丰富的设置中的可访问性，特别是为可访问的$ \ infty $ -cosmoi获得同位固定的结果。
We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category $\mathcal V$ admitting certain limits. When $\mathcal V$ is equipped with the trivial model structure this recaptures the enriched version of Freyd's adjoint functor theorem. For non-trivial model structures, we obtain new adjoint functor theorems of a homotopical flavour - in particular, when $\mathcal V$ is the category of simplical sets we obtain a homotopical adjoint functor theorem appropriate to the $\infty$-cosmoi of Riehl and Verity. We also investigate accessibility in the enriched setting, in particular obtaining homotopical cocompleteness results for accessible $\infty$-cosmoi.
