monoid #card #bidirectional
Category with one object
Can have many morphisms
Known as a sort of “pre-group” in group theory
Monoid in set theory #card #bidirectional
defined as a set of elements
some operation for that set
can take in multiple elements from the set and return one from the set
has to be defined for all elements of the set
one element is the unit element
associative, with a unit element; not necessarily commutative
Examples
multiplication, unit element = 1
string concatenation, unit element = "" (empty string)
appending lists
Monoid in Set Theory == Monoid in Category Theory
[[Monoid]] #card #bidirectional