Skew-monoidal reflection and lifting theorems
Abstract
The Day Reflection Theorem gives conditions under which a reflective subcategory of a closed monoidal category can be equipped with a closed monoidal structure in such a way that the reflection adjunction becomes a monoidal adjunction. We adapt this result to skew monoidal categories. The beauty of this variant is further evidence that the direction choices involved in the skew notion are important for organizing, and adding depth to, certain mathematical phenomena. We also provide conditions under which a skew monoidal structure can be lifted to the category of Eilenberg-Moore algebras for a comonad.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.6972
- arXiv:
- arXiv:1410.6972
- Bibcode:
- 2014arXiv1410.6972L
- Keywords:
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- Mathematics - Category Theory;
- 18D10
- E-Print:
- Roughly the first half on the skew reflection theorem was presented to the Australian Category Seminar on 27 August 2014. Version 2 is 14 pages and includes a title change. There is new material on skew warpings riding an action and a skew-monoidal lifting theorem. Version 3: added reference