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1. • CommentRowNumber1.
   • CommentAuthorKeithEPeterson
   • CommentTimeDec 10th 2016
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   Author: KeithEPeterson
   Format: MarkdownItexI can't help but notice the rose graphs look a lot like the diagrams for one-object categories. Shouldn't I be able to define an isomorphism from one-object categories to rose graphs? Is there any use in taking this approach? If so, what does it say about looping/delooping?

   I can’t help but notice the rose graphs look a lot like the diagrams for one-object categories. Shouldn’t I be able to define an isomorphism from one-object categories to rose graphs? Is there any use in taking this approach? If so, what does it say about looping/delooping?

2. • CommentRowNumber2.
   • CommentAuthorRodMcGuire
   • CommentTimeDec 11th 2016
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   Author: RodMcGuire
   Format: MarkdownItexIs this what you are asking? For a set $A$ are these 2 quivers somehow related to looping/delooping. 1. the discrete quiver with $A$ corresponding to objects and with no edges. 1. the 1 object quiver with $A$ corresponding to the edges. (the free categories on these 2 quivers are a discrete category and a free 1 object monoid on $A$) I would like to know the answer to this.

   Is this what you are asking?

   For a set $A$ are these 2 quivers somehow related to looping/delooping.

   1. the discrete quiver with $A$ corresponding to objects and with no edges.
   2. the 1 object quiver with $A$ corresponding to the edges.

   (the free categories on these 2 quivers are a discrete category and a free 1 object monoid on $A$)

   I would like to know the answer to this.

3. • CommentRowNumber3.
   • CommentAuthorKeithEPeterson
   • CommentTimeDec 11th 2016
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   Author: KeithEPeterson
   Format: MarkdownItexSomeone on another forum made the joke, $\begin{bmatrix} 0 & 1\\ -1 & 0 \end{bmatrix}\cdot8=\infty$. I wanted to see if I could make joke is 'true' if we took $8$ as a literal rose graph. However when looked up [rose graphs](https://upload.wikimedia.org/wikipedia/commons/b/b4/Rose-rhodonea-curve-7x9-chart-improved.svg), the two leaf graph did not exist (or at least not as a figure-eight). The category theorist in me noticed that these curves look like diagrams of one-object categories, so curiosity makes me wonder if rose graphs have a relation to monoids and groups. I know you can map a line to a rose graph, and in some ways, that reminded me of a looping process.

   Someone on another forum made the joke, $\begin{bmatrix} 0 & 1\\ -1 & 0 \end{bmatrix}\cdot8=\infty$. I wanted to see if I could make joke is ’true’ if we took $8$ as a literal rose graph. However when looked up rose graphs, the two leaf graph did not exist (or at least not as a figure-eight). The category theorist in me noticed that these curves look like diagrams of one-object categories, so curiosity makes me wonder if rose graphs have a relation to monoids and groups.

   I know you can map a line to a rose graph, and in some ways, that reminded me of a looping process.

4. • CommentRowNumber4.
   • CommentAuthorKeithEPeterson
   • CommentTimeDec 11th 2016
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   Author: KeithEPeterson
   Format: MarkdownItexActually, yeah. My hunch was right! It's a topological rose, which are topological representations of free groups, though one could enforce an orientation on the loops to make it a monoid. This makes drawing one-object categories much more easier using a rose curve than using Bézier curves from a small dot to itself.

   Actually, yeah. My hunch was right! It’s a topological rose, which are topological representations of free groups, though one could enforce an orientation on the loops to make it a monoid.

   This makes drawing one-object categories much more easier using a rose curve than using Bézier curves from a small dot to itself.