In [lecture 2](https://www.youtube.com/watch?v=jm3bJrULMqM) (about time 5:30), Brendan introduces a notion of **Shape**.

I like this idea. Each Shape (object, pair, arrow, isomorphism) suggests _the essence of_ a basic idea in Category Theory.

An essence is not formally defined. I can play with it in my own way, with tools I'm familiar with.

This is roughly the table that Brendan presented.

```

| Shape Label | Essence Of | Objects | Arrows |

| ----------- | ----------- | ------- | ------ |

| 1 | object | 1 | 1 |

| P | pair | 2 | 2 |

| 2 | arrow | 2 | 3 |

| I | isomorphism | 2 | 4 |

```

[Graphviz](https://graphviz.org/), can roughly reproduce what Brendan drew on the blackboard.

A number of online sites can parse Graphviz .dot notation, and display it as a Scalable Vector Graphics (SVG) image.

[WebGraphviz](http://www.webgraphviz.com/) is one such site. Copy any of the following four _digraph_ lines, paste it into the WebGraphviz site, click _Generate Graph!_, and view the SVG image (as shown below).

digraph 1 {x->x; label="1 object";}

![Figure 1](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/object1.svg?sanitize=true "Figure 1")

digraph P {x->x y->y; label="P pair";}

![Figure P](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/pairP.svg?sanitize=true "Figure P")

digraph 2 {x->x->y->y; label="2 arrow";}

![Figure 2](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/arrow2.svg?sanitize=true "Figure 2")

digraph I {x->x->y->y->x; label="I isomorphism";}

![Figure I](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/isomorphismI.svg?sanitize=true "Figure I")

I wonder what other essences are lurking out there, or is this as far as we can go with this concept?

I like this idea. Each Shape (object, pair, arrow, isomorphism) suggests _the essence of_ a basic idea in Category Theory.

An essence is not formally defined. I can play with it in my own way, with tools I'm familiar with.

This is roughly the table that Brendan presented.

```

| Shape Label | Essence Of | Objects | Arrows |

| ----------- | ----------- | ------- | ------ |

| 1 | object | 1 | 1 |

| P | pair | 2 | 2 |

| 2 | arrow | 2 | 3 |

| I | isomorphism | 2 | 4 |

```

[Graphviz](https://graphviz.org/), can roughly reproduce what Brendan drew on the blackboard.

A number of online sites can parse Graphviz .dot notation, and display it as a Scalable Vector Graphics (SVG) image.

[WebGraphviz](http://www.webgraphviz.com/) is one such site. Copy any of the following four _digraph_ lines, paste it into the WebGraphviz site, click _Generate Graph!_, and view the SVG image (as shown below).

digraph 1 {x->x; label="1 object";}

![Figure 1](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/object1.svg?sanitize=true "Figure 1")

digraph P {x->x y->y; label="P pair";}

![Figure P](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/pairP.svg?sanitize=true "Figure P")

digraph 2 {x->x->y->y; label="2 arrow";}

![Figure 2](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/arrow2.svg?sanitize=true "Figure 2")

digraph I {x->x->y->y->x; label="I isomorphism";}

![Figure I](https://gist.githubusercontent.com/kenwebb/b8a7893bc4723388cd6e355069c9fd55/raw/ca6b84a43225657fbc55fef19c4ccdb473882f2c/isomorphismI.svg?sanitize=true "Figure I")

I wonder what other essences are lurking out there, or is this as far as we can go with this concept?