+++
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: $f \circ I_B = f$, $I_A \circ f = f$