|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Multivariable adjunctions and mates
If you have a question about this talk, please contact Julia Goedecke.
In this talk I will present the notion of ``cyclic double multicategory’’, as a structure in which to organise multivariable adjunctions and mates. The most common example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this situation to $n+1$ functors of $n$ variables. Furthermore, we generalise the mates correspondence, which enables us neatly to pass between natural transformations involving left adjoints and those involving right adjoints.
While the standard mates correspondence is elegantly described using an isomorphism of double categories, the multivariable version needs the framework of ``double multicategories’’. Moreover, we show that the analogous isomorphisms of double multicategories give a cyclic action on the multimaps, yielding the notion of ``cyclic double multicategory’’.
This is joint work with Nick Gurski and Emily Riehl, and is motivated by and applied to Riehl’s approach to algebraic monoidal model categories.
This talk is part of the Category Theory Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsChemical Engineering and Biotechnology Second Language Education Group Computer Laboratory talks
Other talksTechnological Conspiracies Five star American Habitats Maps and seafarers in the English Channel (eighteenth century) Physics of the Cytoskeleton & Morphogenesis (TBC) Ionotropic Glutamate receptors and GABAA receptors; from protein structure to neuronal circuits TBA