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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Garner, Richard and Lack, Stephen 2012. Lex colimits. Journal of Pure and Applied Algebra, Vol. 216, Issue. 6, p. 1372.


    Lucyshyn-Wright, Rory B.B. 2012. Totally distributive toposes. Journal of Pure and Applied Algebra, Vol. 216, Issue. 11, p. 2425.


    Marmolejo, Francisco Rosebrugh, Robert and Wood, R.J. 2012. Completely and totally distributive categories I. Journal of Pure and Applied Algebra, Vol. 216, Issue. 8-9, p. 1775.


    Centazzo, C. and Wood, R.J. 2005. A factorization of regularity. Journal of Pure and Applied Algebra, Vol. 203, Issue. 1-3, p. 83.


    Adámek, Jir̆í and Tholen, Walter 1990. Total categories with generators. Journal of Algebra, Vol. 133, Issue. 1, p. 63.


    Day, Brian and Street, Ross 1986. Categories in which all strong generators are dense. Journal of Pure and Applied Algebra, Vol. 43, Issue. 3, p. 235.


    Street, Ross 1982. Two-dimensional sheaf theory. Journal of Pure and Applied Algebra, Vol. 23, Issue. 3, p. 251.


    Walters, R.F.C. 1982. Sheaves on sites as Cauchy-complete categories. Journal of Pure and Applied Algebra, Vol. 24, Issue. 1, p. 95.


    ×
  • Bulletin of the Australian Mathematical Society, Volume 23, Issue 2
  • April 1981, pp. 199-208

Notions of topos

  • Ross Street (a1)
  • DOI: http://dx.doi.org/10.1017/S000497270000705X
  • Published online: 01 April 2009
Abstract

A Grothendieck topos has the property that its Yoneda embedding has a left-exact left adjoint. A category with the latter property is called lex-total. It is proved here that every lex-total category is equivalent to its category of canonical sheaves. An unpublished proof due to Peter Freyd is extended slightly to yield that a lex-total category, which has a set of objects of cardinality at most that of the universe such that each object in the category is a quotient of an object from that set, is necessarily a Grothendieck topos.

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[2]P.J. Freyd and G.M. Kelly , “Categories of continuous functors, I”, J. Pure Appl. Algebra 2 (1972), 169191.

[5]Ross Street , “Cosmoi of internal categories”, Trans. Amer. Math. Soc. 258 (1980), 271318.

[7]Ross Street and Robert Walters , “Yoneda structures on 2-categories”, J. Algebra 50 (1978), 350379.

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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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