Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
139 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The Relative Monoidal Center and Tensor Products of Monoidal Categories (1803.04403v4)

Published 12 Mar 2018 in math.QA, math.CT, and math.RT

Abstract: This paper develops a theory of monoidal categories relative to a braided monoidal category, called augmented monoidal categories. For such categories, balanced bimodules are defined using the formalism of balanced functors. The two main constructions are a relative tensor product of monoidal categories as well as a relative version of the monoidal center, which are Morita dual constructions. A general existence statement for a relative tensor products is derived from the existence of pseudo-colimits. In examples, a category of locally finite weight modules over a quantized enveloping algebra is equivalent to the relative monoidal center of modules over its Borel part. A similar result holds for small quantum groups, without restricting to locally finite weight modules. More generally, for modules over braided bialgebras, the relative center is shown to be equivalent to the category of braided Yetter-Drinfeld modules (or crossed modules). This category corresponds to modules over the braided Drinfeld double (or double bosonization) which are locally finite for the action of the dual.

Citations (16)

Summary

We haven't generated a summary for this paper yet.