Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/44482
Title: The monads of classical algebra are seldom weakly cartesian
Authors: Clementino, Maria Manuel 
Hofmann, Dirk 
Janelidze, George 
Issue Date: 2013
Publisher: Springer
Project: PEst-C/MAT/UI0324/2011 
Serial title, monograph or event: Journal of Homotopy and Related Structures
Volume: 9
Issue: 1
Abstract: This paper begins a systematic study of weakly cartesian properties of monads that determine familiar varieties of universal algebras. While these properties clearly fail to hold for groups, rings, and many other related classical algebraic structures, their analysis becomes non-trivial in the case of semimodules over semirings, to which our main results are devoted. In particular necessary and sufficient conditions on a semiring S, under which the free semimodule monad has: (a) its underlying functor weakly cartesian, (b) its unit a weakly cartesian natural transformation, (c) its multiplication a weakly cartesian natural transformation, are obtained.
URI: http://hdl.handle.net/10316/44482
Other Identifiers: 10.1007/s40062-013-0063-2
DOI: 10.1007/s40062-013-0063-2
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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