COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Category Theory Seminar > Symmetric monoidal closed categories relative to a base

## Symmetric monoidal closed categories relative to a baseAdd to your list(s) Download to your calendar using vCal - Rory Lucyshyn-Wright
- Tuesday 28 October 2014, 14:15-15:30
- MR5, Centre for Mathematical Sciences.
If you have a question about this talk, please contact Dr Ignacio Lopez Franco. If M and V are symmetric monoidal closed categories, then M may carry an enrichment in V, but we show that such an enrichment is essentially the same as a normal morphism M—> V. We make this precise as an equivalence of 2-categories. Next, we show that this equivalence lifts to an equivalence between 2-categories whose objects are, respectively, (1) tensored symmetric monoidal closed V-categories and (2) symmetric monoidal closed adjunctions with right adjoint valued in V. Further, whereas every normal closed functor carries an enrichment, we show also that (1) and (2) are equivalent to a third 2-category whose objects are adjunctions F -| G : M—> V in the 2-category of symmetric monoidal closed V-categories. Along the way, we study change of base for symmetric monoidal V-categories, and we show that the assignment to each symmetric monoidal closed functor its associated enriched functor is part of a 2-functor valued in an op-fibred 2-category of enriched symmetric monoidal closed 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
- DPMMS lists
- Interested Talks
- MR5, Centre for Mathematical Sciences
- School of Physical Sciences
- bld31
- ndb35's list
- yk373's list
Note that ex-directory lists are not shown. |
## Other listsIntroducing the Cambridge Migration Research Forum (CAMMIGRES): An Event for New Graduates The Yerushah Lecture 2012 Pedagogy, Language, Arts & Culture in Education (PLACE) Group Seminars## Other talksBayesian optimal design for Gaussian process model Aspects of adaptive Galerkin FE for stochastic direct and inverse problems Radiocarbon as a carbon cycle tracer in the 21st century TODAY Adrian Seminar: "Synaptic plasticity and memory" Phylogenetic hypothesis of the Oleeae tribe (Oleaceae) Diversification and molecular evolution patterns in plastid and nuclear ribosomal DNA Propaganda porcelain: The mirror of the Russian revolution and its consequences |