Multivariable adjunctions and mates

Add to your list(s) Download to your calendar using vCal

• Eugenia Cheng, Sheffield
• Tuesday 28 February 2012, 14:15-15:00
• MR5, Centre for Mathematical Sciences.

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:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• Category Theory Seminar
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• MR5, Centre for Mathematical Sciences
• School of Physical Sciences

Note that ex-directory lists are not shown.