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Elementary observations on 2-categorical limits

  • G.M. Kelly (a1)
Abstract

With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important 2-categories fail to be complete but do admit a wide class of limits. Accordingly, we introduce a variety of particular 2-categorical limits of practical importance, and show that certain of these suffice for the existence of indexed lax- and pseudo-limits. Other important 2-categories fail to admit even pseudo-limits, but do admit the weaker bilimits; we end by discussing these.

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[2]J. Bénabou , ‘Introduction to bicategories’, in Lecture Notes in Math. 47, pp. 177 (Springer-Verlag, Berlin, Heidelberg, New York, 1967).

[8]G.M. Kelly , ‘On clubs and doctrines’, in Lecture Notes in Math. 420 (Springer-Verlag, Berlin, Heidelberg, New York, 1974). pp. 181256.

[12]G.M. Kelly and R. Street , ‘Review of the elements of 2-categories’, in Lecture Notes in Math. 420 (Springer-Verlag, Berlin, Heidelberg, New York, 1974). pp. 75103.

[13]R. Street , ‘Elementary Cosmoi I’, in Lecture Notes in Math 420 (Springer-Verlag, Berlin, Heidelberg, New York, 1974). pp. 134180.

[14]R. Street , ‘Limits indexed by category-valued 2-functor’, J. Pure Appl. Algebra 8 (1976), 149181.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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