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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeJul 21st 2010

    New entry (improvized, check co- etc.) resolution.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 21st 2010

    I added a bit, trying to indicate the wider context.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2017
    • (edited Sep 26th 2017)

    I had occasion to link from an exposition that I am writing to the entry homological resolution, only to realize that its content was fairly chaotic. So I tried to give it a more expository helpful Idea-section. The last two paragraphs of what is now the Examples-section there are still in need of improvement, I feel, but I didn’t touch these.

    There was one more paragraph which went on about orbifolds. I felt this didn’t belong to “homological resolution”, but maybe to resolution. Turning there, I found again a very unsatisfactory Idea-section, and so I went ahead and added a few lines that hopefully improve on it a little.

    Then I made sure these entries are cross-linked with simplicial resolution… only to discover – you are guessing it already – that this entry is in bad shape. But I am out of steam now. If anyone feels in expository mood, that entry would be a good place to turn some energy to.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeSep 27th 2017
    • (edited Sep 27th 2017)

    Should mention be given and links made here to comonadic resolutions and even the old step-by-step idea of Michel André, which emphasises the similarity with defining a CW-complex by adding cells to already existing stuff?

    (Edit: Do we have an entry for comonadic resolution under some other name? I found three links but all grey ones and no active one.)

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeSep 27th 2017

    There is the discussion in bar construction but that does not have a lot of the references to the early stuff by Barr and Beck, in the Triples seminar lecture notes, nor the original in Godement and to the extensive work by Duskin. I thought the use of bar’s was due to Eilenberg and Mac Lane.