Ruprecht-Karls-Universität Heidelberg
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„Session 8. Adjoint functors: definitions, properties, the adjoint functor theorem. “
Dr. José Ibrahim Villanueva Gutiérrez, Universität Heidelberg

The notion of adjoint functors turns out to be a little bit more delicate for∞-categories than for 1-categories. Forexample, though one can check the existence of an adjoint functor on the level of enriched homotopy categories of∞-categories, one can not check adjointness of two functors in this way.The goal of this talk is to prove fundamental properties of adjoint functors: uniqueness of an adjoint up to equiv-alence [5.2.1.3-5.2.1.4], possibility to check the adjointness using the unit transformation [5.2.2.8], the fact that leftadjoint preserves colimits [5.2.3.5]. It is important to introduce examples of adjoint functors coming from simplicial model categories and Quillenadjunctions between them [5.2.4.6].Please state the adjoint functor theorem [5.5.2.9] postponing the notion of accesible functor to the next talk.

Dienstag, den 11. Juni 2019 um 11:15 Uhr, in INF 205, SR 3 Dienstag, den 11. Juni 2019 at 11:15, in INF 205, SR 3