* Super comma category [not found] <20090218222112.L22481@mx.nsc.ru> @ 2010-01-07 13:33 ` Serge P. Kovalyov 2010-01-08 16:13 ` Andree Ehresmann 0 siblings, 1 reply; 2+ messages in thread From: Serge P. Kovalyov @ 2010-01-07 13:33 UTC (permalink / raw) To: categories Dear Category Theory gurus, Is there any literature in which MacLane's "super comma category" (Cat./.C) of all small diagrams in a category C is studied in details? Actually I work in its covariant form, where a morphism from a diagram D:X->C to G:Y->C is a pair (e,F) consisting of a functor F:X->Y and a natural transformation e:D->GF. For example, is it known that the embedding of an ordinary comma category Cat/C into Cat./.C preserves colimits? Also there exists a monad (Cat./.-, d, m) on CAT, where d_C takes each C-object X to a discrete diagram {X}, and m represents "drawing" a diagram of diagrams as a diagram. Is its Eilenberg-Moore category isomorphic to some "familiar" construction? Thanks, Serge. [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: Super comma category 2010-01-07 13:33 ` Super comma category Serge P. Kovalyov @ 2010-01-08 16:13 ` Andree Ehresmann 0 siblings, 0 replies; 2+ messages in thread From: Andree Ehresmann @ 2010-01-08 16:13 UTC (permalink / raw) To: Serge P. Kovalyov, categories Dear Serge, An answer to your question is the paper "Decompositions et lax-completions" par Rene Guitart et Luc Van den Bril (Cahiers Top. et Geom. Diff. XVIII-4, 1977, pp. 333-407) where the category is called 'categorie des diagrammes". This paper is freely accessible on the NUMDAM site http://www.numdam.org/numdam-bin/feuilleter?j=CTGDC With my best wishes Andree [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 2+ messages in thread
end of thread, other threads:[~2010-01-08 16:13 UTC | newest] Thread overview: 2+ messages (download: mbox.gz / follow: Atom feed) -- links below jump to the message on this page -- [not found] <20090218222112.L22481@mx.nsc.ru> 2010-01-07 13:33 ` Super comma category Serge P. Kovalyov 2010-01-08 16:13 ` Andree Ehresmann
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