Borceux, Francis
[UCL]
Pedicchio, MC.
Given a small exact category E with finite colimits, we prove that the category Lex(E) of left exact presheaves on E is exact precisely when in E, the equivalence relation generated by a reflexive symmetric relation R is a finite iterate of R. This is in particular the case when E is Noetherian, that is, every ascending chain of subobjects is stationary. When this condition is satisfied and moreover E is a pretopos, Lex(E) becomes a topos. Various examples are given, distinguishing the possible situations. (C) 1999 Elsevier Science B.V. All rights reserved.
| Bibliographic reference |
Borceux, Francis ; Pedicchio, MC.. Left exact presheaves on a small pretopos. In: Journal of Pure and Applied Algebra, Vol. 135, no. 1, p. 9-22 (1999) |
| Permanent URL |
http://hdl.handle.net/2078.1/44651 |
