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## Comments

Hello! We are proceeding very slowly and gently in this course, using a clever trick of Fong and Spivak: instead of discussing

categorieswe are (so far) only discussingpreorders. A preorder is a category where there's at most one morphism from any object \(x\) to any object \(y\). This means that all diagrams in this category commute, making the whole subject much easier. Functors get called "monotone functions", colimits get called "joins" and limits get called "meets". We are now working on monoidal preorders, which are a special case of monoidal categories. We are seeing lots of examples of all these ideas.I look forward to seeing you in the discussions. Questions, comments, answers... all are welcome!

`Hello! We are proceeding very slowly and gently in this course, using a clever trick of Fong and Spivak: instead of discussing _categories_ we are (so far) only discussing _preorders_. A preorder is a category where there's at most one morphism from any object \\(x\\) to any object \\(y\\). This means that all diagrams in this category commute, making the whole subject much easier. Functors get called "monotone functions", colimits get called "joins" and limits get called "meets". We are now working on monoidal preorders, which are a special case of monoidal categories. We are seeing lots of examples of all these ideas. I look forward to seeing you in the discussions. Questions, comments, answers... all are welcome!`