|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 listsVon Hugel Institute's seminar programme: Renewing Catholic Social Thought: An Agenda for the 21st Century'. Cambridge Cell Cycle Club Talks Information Structure
Other talksHuman Papillomavirus Life-Cycle Regulation and Association with Cancer The unknowable, the new reformation, and the rationale for religious freedom: the place of religion in Spencer's philosophy Performance Data Recorders Hippocampal network dynamics underpinning the emergence and persistence of spatial memories Sequential Monte Carlo methods for graphical models Structural and functional characterisation of oxide nanomaterials