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diff --git a/content/zettel/4d2.md b/content/zettel/4d2.md new file mode 100644 index 0000000..a46fe85 --- /dev/null +++ b/content/zettel/4d2.md @@ -0,0 +1,21 @@ ++++ +title = "Objects" +author = "Yann Herklotz" +tags = [] +categories = [] +backlinks = ["4d1"] +forwardlinks = ["4d3", "4d2a"] +zettelid = "4d2" ++++ + +Objects have to have the following properties: + +- For objects A, B, we have "Set" of morphisms: $A \rightarrow_f B$ +- Composition: + $\mathit{Mor}(A, B) \times \mathit{Mor}(B, C) = \mathit{Mor}(A, C)$ +- Identity morphisms: $\mathit{Mor}(A, A)$ + +And morphisms have to follow the following axioms: + +- Association: $(f \circ g) \circ h = f \circ (g \circ h)$ +- Identity: $f \circ I_B = f$, $I_A \circ f = f$ |