Timeline for Factoring a natural transformation through a functor
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21, 2021 at 10:58 | comment | added | varkor | If you don't want uniqueness of the factorisation, you can ask for $L$ just to be full. If it arises via a universal property (without uniqueness), then this is suggestive of a weak (2-)limit as @fosco points out. | |
| Apr 21, 2021 at 5:58 | comment | added | fosco | I think it is a particular case of an inserter, but without uniqueness of the 1-cell; the non-uniqueness instead suggests some sort of (weak) orthogonality condition. | |
| Apr 21, 2021 at 3:39 | comment | added | Ben MacAdam | Yeah it’s a bit weaker than that - I have a 2-monad and three strict algebras of it. The morphism $B$ to $C$ acts like an inserter for every parallel pair of strict algebra homomorphisms. My example certainly isn’t a fully faithful functor - it’s actually a reflector. | |
| Apr 21, 2021 at 2:38 | comment | added | David Roberts♦ | @varkor full faithfulness would mean a unique factorisation | |
| Apr 20, 2021 at 23:13 | comment | added | varkor | Could you clarify what your question is? It sounds like you're asking for $L$ to be fully faithful, so that postcomposition by $L$ induces an isomorphism between 2-cells $L \circ F \Rightarrow L \circ G$ and 2-cells $F \Rightarrow G$. | |
| Apr 20, 2021 at 22:37 | history | asked | Ben MacAdam | CC BY-SA 4.0 |