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Anticategories theory

Let me to share to you a toy construction, that kept me entertained recently. Without a better idea, I dubbed it "theory of anticategories". I constructed it definition-first, starting from abstract definitions and ending with discovering examples of such objects and their relation with groupoids. I enjoyed the process of writing it, and hope someone could enjoy reading it (or glossing it over). Indeed, I understand that it is not something deep, the whole construction was done as entertainment after reading an introduction into category theory. People on Reddit suggested that this construction resembles spans. Indeed, the resemblance is striking! However, I feel that spans theory is much deeper. Seems that I described some special kind of spans. I wrote the original document and drew diagrams using Mathcha editor, but then semi-manually converted it to HTML with Mathjax to post it here. Definition Let's define an anticategory is a collection of Objec…

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