TY - JOUR
T1 - Dualizations and antipodes
AU - Day, Brian
AU - McCrudden, Paddy
AU - Street, Ross
PY - 2003/6
Y1 - 2003/6
N2 - Because an exact pairing between an object and its dual is extraordinarily natural in the object, ideas of R. Street apply to yield a definition of dualization for a pseudomonoid in any autonomous monoidal bicategory as base; this is an improvement on Day and Street, Adv. in Math. 129 (1997), Definition 11, p. 114. We analyse the dualization notion in depth. An example is the concept of autonomous (which, usually in the presence of a symmetry, also has been called "rigid" or "compact") monoidal category. The antipode of a quasi-Hopf algebra H in the sense of Drinfeld is another example obtained using a different base monoidal bicategory. We define right autonomous monoidal functors and their higher-dimensional analogue. Our explanation of why the category Comodf (H) of finite-dimensional representations of H is autonomous is that the Comodf operation is autonomous and so preserves dualization.
AB - Because an exact pairing between an object and its dual is extraordinarily natural in the object, ideas of R. Street apply to yield a definition of dualization for a pseudomonoid in any autonomous monoidal bicategory as base; this is an improvement on Day and Street, Adv. in Math. 129 (1997), Definition 11, p. 114. We analyse the dualization notion in depth. An example is the concept of autonomous (which, usually in the presence of a symmetry, also has been called "rigid" or "compact") monoidal category. The antipode of a quasi-Hopf algebra H in the sense of Drinfeld is another example obtained using a different base monoidal bicategory. We define right autonomous monoidal functors and their higher-dimensional analogue. Our explanation of why the category Comodf (H) of finite-dimensional representations of H is autonomous is that the Comodf operation is autonomous and so preserves dualization.
UR - http://www.scopus.com/inward/record.url?scp=0038379723&partnerID=8YFLogxK
U2 - 10.1023/A:1024236601870
DO - 10.1023/A:1024236601870
M3 - Article
AN - SCOPUS:0038379723
SN - 0927-2852
VL - 11
SP - 229
EP - 260
JO - Applied Categorical Structures
JF - Applied Categorical Structures
IS - 3
ER -