Codescent objects and coherence

Stephen Lack*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


We describe 2-categorical colimit notions called codescent objects of coherence data, and lax codescent objects of lax coherence data, and use them to study the inclusion, T-Algs → Ps-T-Alg, of the 2-category of strict T-algebras and strict T-morphisms of a 2-monad T into the 2-category of pseudo T-algebras and pseudo T-morphisms; and similarly the inclusion T-Algs → Lax-T-Alg, where Lax-T-Alg has lax algebras and lax morphisms rather than pseudo ones. We give sufficient conditions under which these inclusions have left adjoints. We give sufficient conditions under which the first inclusion has left adjoint for which the components of the unit are equivalences, so that every pseudo algebra is equivalent to a strict one.

Original languageEnglish
Pages (from-to)223-241
Number of pages19
JournalJournal of Pure and Applied Algebra
Issue number1-3
Publication statusPublished - 8 Nov 2002
Externally publishedYes


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