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Lex colimits

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Amongst the range of structures it has been found mathematically useful to impose upon a category, we find a number which share the following form. There are required the provision of finite limits, of colimits from some specified class, and of certain compatibilities—-or “exactnesses”—-between the finite limits and the colimits. Some typical examples are the notions of regular, or Barr-exact, or lextensive, or adhesive, or coherent, or geometric category. This talk will describe joint work with Steve Lack which accounts for these similiarities, by exhibiting all such notions as particular instances of one common one—-that of cocompleteness with respect to a class of colimits “in the left exact world”.

This talk is part of the Category Theory Seminar series.

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