A note on a free group. The decomposition of a free group functor through the category of heaps

A note on a free group. The decomposition of a free group functor through the category of heaps

This note aims to introduce a left adjoint functor to the functor which assigns a heap to a group. The adjunction is monadic. It is explained how one can decompose a free group functor through the previously introduced adjoint and employ it to describe a slightly different construction of free groups.

___

  • R. Baer, Zur einfuhrung des scharbegriffs, J. Reine Angew. Math., 160 (1929),199-207.
  • M. Barr and C. Wells, Toposes, triples and theories, Corrected reprint of the 1985 original Repr. Theory Appl. Categ., 12 (2005), 1-288.
  • G. M. Bergman, An Invitation to General Algebra and Universal Constructions, Springer, Cham, Second Edition, 2015, available online, https://math.berkeley.edu/ gbergman/245/3.2.pdf.
  • T. Brzezinski, Trusses: paragons, ideals and modules, J. Pure Appl. Algebra, 224(6) (2020), 106258 (39 pp).
  • T. Brzezinski and B. Rybolowicz, Modules over trusses vs modules over rings: direct sums and free modules, Algebr. Represent. Theory, 25(1) (2022), 1-23.
  • D. S. Dummit and R. M. Foote, Abstract Algebra, Prentice Hall, 1991.
  • W. Dyck, Gruppentheoretische studien, Math. Ann., 20(1) (1882), 1-44.
  • S. Mac Lane, Categories for the Working Mathematician, Springer, New York, Second Edition, 1998.
  • H. Prufer, Theorie der abelschen gruppen, Math. Z., 20(1) (1924), 165-187.