Enhanced 2-categorical structures, two-dimensional limit sketches and the symmetry of internalisation
| Autor: | Arkor, Nathanael, Bourke, John, Ko, Joanna |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Many structures of interest in two-dimensional category theory have aspects that are inherently strict. This strictness is not a limitation, but rather plays a fundamental role in the theory of such structures. For instance, a monoidal fibration is - crucially - a strict monoidal functor, rather than a pseudo or lax monoidal functor. Other examples include monoidal double categories, double fibrations, and intercategories. We provide an explanation for this phenomenon from the perspective of enhanced 2-categories, which are 2-categories having a distinguished subclass of 1-cells representing the strict morphisms. As part of our development, we introduce enhanced 2-categorical limit sketches and explain how this setting addresses shortcomings in the theory of 2-categorical limit sketches. In particular, we establish the symmetry of internalisation for such structures, entailing, for instance, that a monoidal double category is equivalently a pseudomonoid in an enhanced 2-category of double categories, or a pseudocategory in an enhanced 2-category of monoidal categories. Comment: 49 pages |
| Databáze: | arXiv |
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