| M. Kelly. Doctrinal adjunction. Lecture Notes in Math. 420, pp. 257-280, 1974. |
....F : induces a 2 functor F : MonCat is equipped with a 2 categorical structure by defining 2 cells in it as monoidal natural transformations ( EiKe66] The process ( of sending to and F to F extends to a 2 functor from MonCat to 2 Cat . Adjunctions in MonCat were characterised in [Kel74]. Moving to the case of enrichments over bicategories, several notions of morphism between bicategories were proposed in the literature, but no analogous 2 functor ( was known in this situation. Two sided enrichments are a slight generalisation of monoidal functors and Benabou s lax functors ....
G.M. Kelly, Doctrinal adjunction, Lecture Notes in Math. 420 (1974), 257-280
....a 2 functor F : V Cat W Cat. MonCat is equipped with a 2 categorical structure by de ning 2 cells in it as monoidal natural transformations ( EiKe66] The process ( of sending V to V Cat and F to F extends to a 2 functor from MonCat to 2 Cat. Adjunctions in MonCat were characterised in [Kel74]. Moving to the case of enrichments over bicategories, several notions of morphism between bicategories where proposed in the literature, but adjoints were not preserved by ( A two sided enrichment F : V W between two bicategories was proposed in [KLSS99] as a slight generalisation of ....
G.M. Kelly, Doctrinal adjunction, Lecture Notes in Math. 420 Springer-Verlag, Berlin, 74, 257-280
....a tiling is a special case of a honeycomb, but we reserve the last term for the case when the cell or the vertex figure is a star polytope and so the honeycomb covers the space several times; the multiplicity of the covering is called its density. Embedding of Platonic solids was remarked in [Kel75] and precised, for the dodecahedron, in [ADe80] Then [Ass81] showed that 36, 63, and mk (for even m 8 and m = 1) are embeddable. The remaining case of odd m and limit cases of m = 2; 1 was decided in [DSt96] all those results are put together in the Theorem 1 below. All four star polyhedra are ....
J.B.Kelly, Hypermetric spaces, Lecture Notes in Math. 490, Springer-Verlag, Berlin (1975) 17--31.
....lax G ring categories is denoted G Gamma Rng(Cat) and the 2 category of (strict) G ring categories is denoted G Gamma RngCat. Theory and Applications of Categories, Vol. 3, No. 4 58 2.4. Examples. i) Let SymBiMon be the 2 category with 0 cells the symmetric bimonoidal categories (see LaPlaza [9], except that here we assume distributivity isomorphisms) We also have the 2 category BrBiMon having 0 cells the braided bimonoidal categories. It contains SymBiMon as a full sub 2 category. Similarly the 2 category BiPerm with 0 cells the bipermutative categories is a full sub 2 category of ....
G.M. Kelly, M. LaPlaza, G. Lewis and S. MacLane, Coherence in Categories, Lecture Notes in Math. 281, Springer, Berlin, 1972.
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M. Kelly. Doctrinal adjunction. Lecture Notes in Math. 420, pp. 257-280, 1974.
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