Cf: Peirce's Categories • 17
At: https://inquiryintoinquiry.com/2020/05/07/peirces-categories-%e2%80%a2-17/
Helmut, List ...
I did not get to Helmut's question about reducibility so I added a link
to an article on that, plus a few more giving background and examples for
sign relations, triadic relations, and finitary (or polyadic) relations
in general.
Helmut Raulien asked several questions about the composition, irreducibility, and reducibility of relations. For
background on relation composition as Peirce originally treated it, I referred him to Peirce's 1870 Logic Of Relatives,
especially the section titled “The Signs for Multiplication”, along with my commentary linked below.
• Peirce's 1870 Logic Of Relatives
https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview
There is also this article:
• Relation Composition
https://oeis.org/wiki/Relation_composition
For readers who want to skip to the chase for the quickest possible overview, the sorts of pictures floating through my
head when I'm thinking about relational composition are the bipartite graph or “bigraph” pictures in the following section.
• Relation Composition • Graph-theoretic Picture
https://oeis.org/wiki/Relation_composition#Graph-theoretic_picture
The ways in which relations are reducible or irreducible to simpler relations
are covered in the following article.
• Relation Reduction
https://oeis.org/wiki/Relation_reduction
The following set of articles, in order of increasing generality, may be useful on these scores, providing background
and concrete examples.
• Sign Relations
https://oeis.org/wiki/Sign_relation
• Triadic Relations
https://oeis.org/wiki/Triadic_relation
• Relation Theory
https://oeis.org/wiki/Relation_theory
Resources
=========
• Precursors Of Category Theory
https://oeis.org/wiki/Precursors_Of_Category_Theory
• Survey of Precursors Of Category Theory
https://inquiryintoinquiry.com/2015/05/15/survey-of-precursors-of-category-theory-%e2%80%a2-1/
Regards,
Jon
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