All Questions
Tagged with 2-categories kan-extension
7 questions
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Existence and characterisations of left Kan extensions and liftings in the bicategory of relations II
This is the second part to a previous question regarding left Kan extensions/lifts in the bicategory $\mathsf{Rel}$ of sets, relations, and inclusions of relations, which has now been split into two ...
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Existence and characterisations of left Kan extensions and liftings in the bicategory of relations I
The bicategory $\mathsf{Rel}$ of sets, relations, and inclusions of relations has right Kan extensions and right Kan lifts¹, however I believe it does not have all left Kan extensions/lifts.
Is it ...
- 11.8k
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Adjoining extensions in bicategories
Given a bicategory $\mathcal K$, is there a universal construction of a bicategory $\mathcal K'$ and faithful locally fully faithful pseudofunctor $\mathcal K \hookrightarrow \mathcal K'$ such that ...
- 10.7k
4
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Coherence for closed bicategories
A right-closed bicategory [1] is a bicategory that has all right extensions (i.e. right adjoints to precomposition with a fixed 1-cell). A one-object right-closed bicategory is therefore a right-...
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3
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Reference for "taking adjuncts preserves Kan extensions"
I'm using a result similar to the one below, and I would like to know if there is a reference that I can cite. It's easily proved, by "following your nose". The cell $G\phi.\eta_A$ is often ...
- 383
7
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Left Kan extensions of "strong" monoidal functors
Consider the 2-category $\mathsf{MonCat}$ where objects are monoidal categories,
1-cells are strong monoidal functors, and 2-cells are monoidal natural transformations.
Given arrows $f: \mathsf{C} \to ...
7
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2
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Kan extensions in concrete 2-categories
Kan extensions make sense in any 2-category. I am interested in Kan extensions in "concrete" 2-categories consisting of actual categories with some sort of structure (e.g., finite products, finite ...
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