Changes between Initial Version and Version 1 of Ticket #18175, comment 20
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 05/31/15 06:14:57 (4 years ago)
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Ticket #18175, comment 20
initial v1 1 1 It still seems like we are having an assumption that all manifolds can inherently be realized over '''R'''. This was my initial assumption too, and so manifolds that could be locally homoemorphic to '''C'''^d^ were a special case. 2 2 3 However I feel like it would be best for `Manifolds` to be over an arbitrary topological field (which will require some very mild changes). So then the heirarchy for manifolds thenbe:3 However I feel like it would be best for `Manifolds` to be over an arbitrary topological field (which will require some very mild changes). So then the heirarchy for manifolds would be: 4 4 {{{ 5 5 Manifolds … … 13 13 Complex 14 14 }}} 15 Do we think we should add a stub category for PL and/or (pseudo) Riemannian manifolds? How about `ManifoldsWithBoundary` as a supercategory of `Manifolds` (and how many of these extra structures lift to the boundary)? 15 Do you think this what we want? 16 17 Also do we think we should add a stub category for PL and/or (pseudo) Riemannian manifolds? How about `ManifoldsWithBoundary` as a supercategory of `Manifolds` (and how many of these extra structures lift to the boundary)? 16 18 17 19 A question for CW complexes, should the elements of a CW complex be the cells or the points of the topological space? Right now, I'm taking the former approach, but I feel this might be an abuse as these should be subobjects of the category (Nicolas, any wisdom to impart on this?). If this seems like a nontrivial issue, I can split this ticket into 2 parts; one for the manifolds and one for the CW complexes.