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• Free monoid generated by
  : Be sure to check [[Discussion of the free monoid and free semigroup generated by a set]], as there are some things to note Given a [[set]], {{M|X}}, there is a ''free'' [[monoid]], {{M|(F,*)}}{{rAAPAG}}.
  2 KB (419 words) - 16:20, 20 July 2016
• Free semigroup generated by
  ...re semgroups), however there is a difference, see [[Discussion of the free monoid and free semigroup generated by a set]] ...by]] (which of course is also a semigroup) - see [[discussion of the free monoid and free semigroup generated by a set]]){{rAAPAG}}, defined as follows:
  1 KB (200 words) - 07:07, 21 July 2016
• Semigroup
  ...rade=A|msg=Demote once it has been fleshed out (to at least in line with [[monoid]])}} : '''Note: ''' not to be confused with [[monoid|monoids]] and [[group|groups]]. Note all groups are monoids and all monoids
  631 B (99 words) - 07:27, 21 July 2016
• Omega(X,b)
  {{Caution|This is not a [[monoid]] or even a [[semigroup]] as {{M|*}} is not [[associative]]. See [[#Caveats {{Definition|Algebraic Topology|Homotopy Theory|Topology|Functional Analysis}}
  2 KB (364 words) - 04:47, 3 November 2016
• Polynomial u-ring
  * Let {{M|M:\eq\{e,X,X^2,X^3,\ldots,X^n,\ldots\} }} be the [[free monoid generated by]] {{M|\{X\} }}. #* But this requires a few things: [[the cardinality of the free monoid generated by a single object is countable]] and [[finitely many elements re
  3 KB (643 words) - 02:34, 20 November 2016
• A continuous map induces a homomorphism on fundamental groups
  ...|p\in X}}. There is an operation, [[loop concatenation]], but it isn't a [[monoid]] or even a [[semigroup]] yet! As concatenation is not associative</ref> is {{Theorem Of|Topology|Algebraic Topology|Homotopy Theory}}
  8 KB (1,475 words) - 07:35, 14 December 2016