# Week 7

## Schedule

Summary | Solutions | Time (min) |
---|---|---|

Lecture 8 | ||

* monoidal preorder (3:15) | ||

* category (3:40) | ||

* monoidal category (4:23) | ||

* wiring diagrams (5:35) | ||

* coherence conditions (11:11) | ||

* symmetric monoidal category (12:00) | ||

* functoriality of \(\otimes\) (24:15) | ||

* categorification (30:45) | ||

* natural isomorphism (33:00) | ||

* \(\mathbf{Prof}_\mathbf{Bool}\) (35:18) | ||

* dual objects (48:48) | ||

* compact closed category (51:38) | ||

SSC: Chapter 4 | * EX 4.31 | 10 |

* \(\mathbf{Prof}_\mathcal{V}\) (T 4.23) | * EX 4.36 | 5 |

* \(\mathbf{Prof}_\mathbf{Bool}\) (D 4.24) | * EX 4.38 | 5 |

* unit profunctor is identity on composition (L 4.27) | ||

* serial composition of profunctors (L 4.31) | ||

* companions & conjoints (D 4.34) | ||

* | ||

Total | 20 |