论文信息 - KAN EXTENSIONS AND LAX IDEMPOTENT PSEUDOMONADS

KAN EXTENSIONS AND LAX IDEMPOTENT PSEUDOMONADS

We show that colax idempotent pseudomonads and their algebras can be presented in terms of right Kan extensions. Dually, lax idempotent pseudomonads and their algebras can be presented in terms of left Kan extensions. We also show that a distributive law of a colax idempotent pseudomonad over a lax idempotent pseudomonad has a presentation in terms of Kan extensions.

F. Marmolejo | R. J. Wood | F. Marmolejo

[1] Jonathon Funk,et al. Singular Coverings of Toposes , 2006 .

[2] A. Kock. Monads for which Structures are Adjoint to Units , 1995 .

[3] S. Lack,et al. The formal theory of monads II , 2002 .

[4] F. Marmolejo,et al. Coherence for pseudodistributive laws revisited. , 2008 .

[5] V. E. Cazanescu. Algebraic theories , 2004 .

[6] An extension of the regular completion , 2002 .

[7] Robert Rosebrugh,et al. A basic distributive law , 2002 .

[8] F. Marmolejo,et al. MONADS AS EXTENSION SYSTEMS |NO ITERATION IS NECESSARY , 2010 .

[9] Marta Bunge. Coherent extensions and relational algebras , 1974 .

[10] F. Marmolejo,et al. Distributive laws for pseudomonads. , 1999 .

[11] Volker Zöberlein,et al. Doctrines on 2-categories , 1976 .

[12] Robert Rosebrugh,et al. Completely and totally distributive categories I , 2012 .

[13] A categorical approach to universal algebra , 1970 .

[14] F. Marmolejo. Doctrines Whose Structure Forms a Fully Faithful Adjoint String , 1997 .