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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 9th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownSpent all day with being distracted from this single thing that I planned to finish this morning: now at least a rough sketch is done at [[infinitesimal interval object]] in the last section with the long section name I mean to define the "infinitesimal singular simplicial complex" in a new way. Anders Kock defines this guy for "formal manifols", roughly, for spaces that have an atlas by vector spaces. There the simple definition applies recalled at [[infinitesimal singular simplicial complex]]. But there should be a definition for arbitrary [[microlinear space]]s, And it should be such that it is almost manfestly the inifnitesimal version of the path oo-groupoid construction described at [[interval object]]. This is what I am aiming to describe here. One crucial thing is that we want that morphisms out of the objects in degree k of the infinitesimal singular simplicial complex that vanish on degenerate k-simplices are automatically fiberwise skew-linear. Seeing this in the construction that I am presenting there seems to be different to the way Anders Kock describes it in the other setup. This is the main thing I need to check again when i am more awake.

   Spent all day with being distracted from this single thing that I planned to finish this morning: now at least a rough sketch is done

   at infinitesimal interval object in the last section with the long section name I mean to define the "infinitesimal singular simplicial complex" in a new way.

   Anders Kock defines this guy for "formal manifols", roughly, for spaces that have an atlas by vector spaces. There the simple definition applies recalled at infinitesimal singular simplicial complex.

   But there should be a definition for arbitrary microlinear spaces, And it should be such that it is almost manfestly the inifnitesimal version of the path oo-groupoid construction described at interval object. This is what I am aiming to describe here.

   One crucial thing is that we want that morphisms out of the objects in degree k of the infinitesimal singular simplicial complex that vanish on degenerate k-simplices are automatically fiberwise skew-linear. Seeing this in the construction that I am presenting there seems to be different to the way Anders Kock describes it in the other setup. This is the main thing I need to check again when i am more awake.