bio | website | maths.mq.edu.au/~slack |
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location | Sydney, Australia | |
age | ||
visits | member for | 4 years, 9 months |
seen | Jun 4 '13 at 12:16 | |
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comment |
Why do filtered colimits commute with finite limits?
Thanks, Dylan. I agree that J being filtered will have to be used. But what properties of Set should be used? |
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answered | Topos associated to a category |
Jan
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comment |
Finitary mono preserving functors on varieties that fail to preserve intersections.
An empty intersection of subobjects is the whole object, so is always preserved. The example I gave involved failure to preserve a binary intersection. Perhaps it would be helpful if you explained what you were really after. |
Jan
10 |
comment |
Finitary mono preserving functors on varieties that fail to preserve intersections.
Rob, I'm not sure quite what this means. I take it that the modified version sends everything to 1? In that case the empty set will no longer possess an algebra structure. |
Jan
9 |
comment |
Finitary mono preserving functors on varieties that fail to preserve intersections.
The endofunctor T of Set sending a set X to a singleton 1 if it is non-empty, and to the empty set 0 if it is empty preserves monomorphisms, since it sends every map to a monomorphism. But it does not preserve the intersection of the two maps from a singleton 1 to a two-element set 2. |
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