Difference between revisions of "Yoneda Lemma"
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{{WikiEntry|key=Yoneda Lemma|qCode=320577}}, in Chinese: (米田引理). It is a theorem that embeds a locally small category into a category of functors. | {{WikiEntry|key=Yoneda Lemma|qCode=320577}}, in Chinese: (米田引理). It is a theorem that embeds a locally small category into a category of functors. | ||
=Symmetry and Relations= | |||
{{:Symmetry and Relations}} | |||
==陳述== | ==陳述== | ||
設<math>\mathcal{C}</math>為一[[範疇 (數學)|範疇]]，定義兩個[[函子範疇]]如下： | 設<math>\mathcal{C}</math>為一[[範疇 (數學)|範疇]]，定義兩個[[函子範疇]]如下： | ||
: <math>\mathcal{C}^\wedge := \mathrm{Fct}(\mathcal{C}, \mathbf{Set})</math> | : <math>\mathcal{C}^\wedge := \mathrm{Fct}(\mathcal{C}, \mathbf{Set})</math> | ||
: <math>\mathcal{C}^\vee := \mathrm{Fct}(\mathcal{C}^{\mathrm{op}}, \mathbf{Set})</math> | : <math>\mathcal{C}^\vee := \mathrm{Fct}(\mathcal{C}^{\mathrm{op}}, \mathbf{Set})</math> | ||
Revision as of 17:04, 24 February 2022
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]:
1. Mathematical objects are completely determined by their relationships to other objectsCite error: Invalid<ref>tag; invalid names, e.g. too many. 2. The properties of a mathematical object are more important than its definitionCite error: Invalid<ref>tag; invalid names, e.g. too many.
The two statements above show that Double-Entry Bookkeeping is a numeric version of content invariance/symmetry over time.
