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DTSTAMP:20260720T061540Z
DESCRIPTION:Title: Coequalizers and free triples\, II (continued)\n\nAbstra
 ct: This paper studies a category X with an endofunctor T : X o X. A T-alg
 ebra is given by a morphism Tx o x in X. We examine the related questions 
 of when T freely generates a triple (or monad) on X\; when an object x in 
 X freely generates a T-algebra\; and when the category of T-algebras has c
 oequalizers and other colimits. The paper defines a category of ``T-horns'
 ' which effectively contains X as well as all T-algebras. It is assume tha
 t Xs is cocomplete and has a factorization system (E\,M) satisfying reason
 able properties. An ordinal-indexed sequence of T-horns is then defined wh
 ich provides successive approximations to a free T-algebra generated by an
  object x in X\, as well as approximations to coequalizers and other colim
 its for the category of T-algebras. Using the notions of an M-cone and a s
 eparated T-horn it is shown that if X is M-well-powered\, then the ordinal
  sequence stabilizes at the desired free algebra or coequalizer or other c
 olimit whenever they exist. This paper is a successor to a paper written b
 y the first author in 1970 that showed that T generates a free triple when
  every x in X generates a free T-algebra. We also consider colimits in tri
 ple algebras and give some examples of functors T for which no x in X gene
 rates a free T-algebra.\n
DTSTART:20191029T183000Z
DTEND:20191029T193000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:M. Barr\, McGill
URL:https://www.mcgill.ca/mathstat/channels/event/m-barr-mcgill-302022
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