https://en.wikipedia.org/wiki/Outline_of_category_theory
https://en.wikipedia.org/wiki/Category_theory#Historical_notes Eilenberg and Mac Lane later wrote that their goal was to understand natural transformations. That required defining functors, which required categories.
https://en.wikipedia.org/wiki/Category_theory#Historical_notes Certain categories called topoi (singular topos) can even serve as an alternative to axiomatic set theory as a foundation of mathematics
category functor: arrow between categories https://ncatlab.org/nlab/show/full+subcategory some objects but all the morphisms between these objects This means at least that ι is a fully faithful functor
more general to more specific following the laws the categories abide TODO how to describe a Category being composed of a Category -> use product? how to describe a Category being an instance of other categories how to describe an object that is a subobject from a different category? (e.g. ideal is subset of ring (not subring))
the arrows between "categories" here are inheritance arrows that can be seen as a functor from category to subcategory (there may be other arrows to represent non inheritent relations) the arrows between objects in the categories are morphisms an object is an instance of a category: the category is represented by a cluster and the object is a node in it or subcluster a node in the object subcluster is an element
// at top-level, category, functor, natural transformation, (binary relation -> order, function, (equivalence relation -> quotient object), binary operation -> algebraic structure), (collection of objects -> topology)
graphviz https://www.graphviz.org/doc/info/attrs.html
Open in Chrome:
file:///Users/fss/Dropbox/Documents/category-theory-graphviz/algebraic-structure.svg
to make svg from dot file
dot -Tsvg algebraic-structure.dot > algebraic-structure.svg
once svg generated add highlights inside <svg>
https://gist.github.com/sverweij/93e324f67310f66a8f5da5c2abe94682?short_path=1afa5af
<style>
/* the lines within the edges */
.edge:active path,
.edge:hover path {
stroke: fuchsia;
stroke-width: 3;
stroke-opacity: 1;
}
/* arrows are typically drawn with a polygon */
.edge:active polygon,
.edge:hover polygon {
stroke: fuchsia;
stroke-width: 3;
fill: fuchsia;
stroke-opacity: 1;
fill-opacity: 1;
}
/* If you happen to have text and want to color that as well... */
.edge:active text,
.edge:hover text {
fill: fuchsia;
}
</style>