Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/189989
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- Title
- Doubles for monoidal categories
- Related
- Theory and applications of categories, Vol. 21, No. 4, (2008), p.61-75
- Related
- http://www.tac.mta.ca/tac/volumes/21/4/21-04abs.html
- Publisher
- Mount Allison University, Department of Mathematics and Science
- Date
- 2008
- FoR/RFCD Code(s)
-
010100 Pure Mathematics
- Author/Creator
- Pastro, Craig Antonio
- Author/Creator
- Street, Ross
- Description
- In a recent paper, Daisuke Tambara defined two-sided actions on an endomodule (= endodistributor) of a monoidal V-category A. When A is autonomous (= rigid = compact), he showed that the V-category (that we call Tamb(A)) of so-equipped endomodules (that we call Tambara modules) is equivalent to the monoidal centre Z[A,V] of the convolution monoidal V-category [A, V]. Our paper extends these ideas somewhat. For general A, we construct a promonoidal V-category DA (which we suggest should be called the double of A) with an equivalence of [DA, V] with Tamb(A). When A is closed, we define strong (respectively, left strong) Tambara modules and show that these constitute a V-category Tamb_s(A) (respectively, Tamb_{ls}(A)) which is equivalent to the centre (respectively, lax centre) of [A, V]. We construct localizations D_sA and D_{ls}A of DA such that there are equivalences of Tamb_s(A) with [D_sA, V] and of Tamb_{ls}(A) with [D_{ls}A, V]. When A is autonomous, every Tambara module is strong; this implies an equivalence of Z[A, V] with [DA,V].
- Description
- 15 page(s)
- Subject Keyword
- 010100 Pure Mathematics
- Subject Keyword
- monoidal centre
- Subject Keyword
- Drinfeld double
- Subject Keyword
- monoidal category
- Subject Keyword
- Day convolution
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Mathematics
- Identifier
- http://hdl.handle.net/1959.14/189989
- Identifier
- ISSN:1201-561X
- Identifier
- mq-rm-2008001399
- Language
- eng
- Reviewed
