Difference between revisions of "Universal property"

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{{WikiEntry|key=Universal property|qCode=1417809}}, also known as [[Universal construction]], is an ideal pervasive in the literature of [[Category Theory]]. This ideal, or the thesis of [[Category Theory]], offered a very different approach to organize knowledge. It is different in a way that it claims all things, all phenomenon came from a single, universal source. This claim indicates that if you master the mechanisms of how this single universal construct generate individual things, all things come from this single idea. That means you don't need to study anything else, since all of them are just variants or descendants of this [[universal construct]]. [[wikipedia:John Henry Newman|Saint John Henry Newman]] who argued for all knowledge, including theology must be taught in a university, may have thought about the following logical argument, too.  
{{WikiEntry|key=Universal property|qCode=1417809}}, also known as [[Universal construction]], is a crucial concept pervasive in the literature of [[Category Theory]]. This concept, or the thesis of [[Category Theory]], offered a very different approach to organize knowledge. According to [[John Peloquin|Peloquin]]<ref name="PeloquinUniversalProperty">{{:Video/Category Theory Part 3 of 3: Universal Properties}}</ref>:
A universal property characterizes an object in a category, in an essentially [[unique]] way, in terms of its relation to other objects through arrows.
The statement shown above used a critical term, [[unique]]. It implies that all things, all phenomenon, if they were to be characterized uniquely, the unique way can be determined by the relation of the object to all other things<ref>See [[Yoneda lemma]]</ref>. For staters, the uniqueness of relations may be verified using [[product]], [[co-product]], [[exponential]], and other kind of arithmetic constructs. [[HandWiki]] has a detailed entry on the subject of [https://handwiki.org/wiki/Universal_property|Universal property], explaining the concept of [[universal morphism]].
 
This implication portrait a single, generalized relational mechanisms to define properties of individual things. All things can be characterized through relations with other things. This relationally-based approach means that you don't need to study anything else, unique properties of every individual can be universally represented using nothing but relations. All properties are just variants or descendants of this relational [[universal construct]]. [[John Peloquin|Peloquin]]<ref extends="PeloquinUniversalProperty">[https://youtu.be/bPvWEN8UGuo?t=66 ...'avoid repeating the same proofs over and over again...']</ref>:
It allows us to avoid repeating the same proofs over and over again in different categories.
By not repeating oneself, it means we can apply this proven theory to generalize many kinds of proven results. This kind generalization, can be thought of as a rigorous belief mechanism, a [[universal construct]].
 
Using the phrase:[[universal construct]], [[wikipedia:John Henry Newman|Saint John Henry Newman]] who argued for all knowledge, including theology must be taught in a university, may have thought about the following logical argument, too. He stated:
  If all things are descendants from a certain universal construct, religions must be derived from such construct.
  If all things are descendants from a certain universal construct, religions must be derived from such construct.
The notion of utilizing [[universal construct]] to bridge understanding between different domain knowledge has been explicitly articulated by [[Olivia Caramello]]. She has several videos on this subject by Olivia Caramello<ref>{{:Video/Unification and morphogenesis}}</ref><ref>{{:Video/The idea of 'bridge' and its unifying role}}</ref><ref>{{:Book/Political Numeracy}}</ref>.
The notion of utilizing [[universal construct]] to bridge understanding between different domain knowledge has been explicitly articulated by [[Olivia Caramello]]. She has several videos on this subject by Olivia Caramello<ref>{{:Video/Unification and morphogenesis}}</ref><ref>{{:Video/The idea of 'bridge' and its unifying role}}</ref><ref>{{:Book/Political Numeracy}}</ref>.


There are a few videos<ref>{{:Video/Category Theory Part 3 of 3: Universal Properties}}</ref><ref>{{:Video/What are...universal properties?}}</ref><ref>{{:Video/Universal Properties}}</ref> on Universal Properties.
There are a few videos<ref name="PeloquinUniversalProperty"/><ref>{{:Video/What are...universal properties?}}</ref><ref>{{:Video/Universal properties}}</ref> on Universal Properties.
{{#ask: [[Category:Universal Property]]
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Latest revision as of 03:09, 24 March 2022

Universal property(Q1417809), also known as Universal construction, is a crucial concept pervasive in the literature of Category Theory. This concept, or the thesis of Category Theory, offered a very different approach to organize knowledge. According to Peloquin[1]:

A universal property characterizes an object in a category, in an essentially unique way, in terms of its relation to other objects through arrows.

The statement shown above used a critical term, unique. It implies that all things, all phenomenon, if they were to be characterized uniquely, the unique way can be determined by the relation of the object to all other things[2]. For staters, the uniqueness of relations may be verified using product, co-product, exponential, and other kind of arithmetic constructs. HandWiki has a detailed entry on the subject of property, explaining the concept of universal morphism.

This implication portrait a single, generalized relational mechanisms to define properties of individual things. All things can be characterized through relations with other things. This relationally-based approach means that you don't need to study anything else, unique properties of every individual can be universally represented using nothing but relations. All properties are just variants or descendants of this relational universal construct. PeloquinCite error: Invalid <ref> tag; invalid names, e.g. too many:

It allows us to avoid repeating the same proofs over and over again in different categories.

By not repeating oneself, it means we can apply this proven theory to generalize many kinds of proven results. This kind generalization, can be thought of as a rigorous belief mechanism, a universal construct.

Using the phrase:universal construct, Saint John Henry Newman who argued for all knowledge, including theology must be taught in a university, may have thought about the following logical argument, too. He stated:

If all things are descendants from a certain universal construct, religions must be derived from such construct.

The notion of utilizing universal construct to bridge understanding between different domain knowledge has been explicitly articulated by Olivia Caramello. She has several videos on this subject by Olivia Caramello[3][4][5].

There are a few videos[1][6][7] on Universal Properties.

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