Yoneda Lemma

Yoneda Lemma(Q320577), in Chinese: (米田引理). It is a theorem that embeds a locally small category into a category of functors.

Symmetry and Relations

To realize why Double Entry Bookkeeping is grounded in many profound ideas, one may start with Yoneda Lemma, a concept that can be summarized as Tai-Danae Bradley's statements on her blog:

1. Mathematical objects are completely determined by their relationships to other objects.
2. The properties of a mathematical object are more important than its definition.

The two statements above show that Double-Entry Bookkeeping is a numeric version of content invariance/symmetry over time.

陳述

設${\mathcal {C}}$為一範疇，定義兩個函子範疇如下：

${\mathcal {C}}^{\wedge }:=\mathrm {Fct} ({\mathcal {C}},\mathbf {Set} )$

${\mathcal {C}}^{\vee }:=\mathrm {Fct} ({\mathcal {C}}^{\mathrm {op} },\mathbf {Set} )$