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Results tagged with ag.algebraic-geometry
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user 4262
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
4
votes
Accepted
When is a colimit of a subcollection the same as the overall colimit?
Dylan's comment is right. More generally, if $D \colon J \to C$ is a diagram and $L \colon J' \to J$ a functor, then the colimit of D is isomorphic to the colimit of DL if and only if L is (co)final. …
- 3,622
13
votes
Why does Hom need an identity in the definition of the category?
As Fernando points out, you can't talk about isomorphisms in a semicategory, which means that they won't be as much use as categories in describing universes of mathematical objects. But the category …
- 3,622
1
vote
Double Direct Systems and Switching of Direct Limits
Your indices are hard to read, and I think you might have mixed some of them up.
If you mean what I think you mean, then Mac Lane's result is exactly what you need. The two colimits are canonically …
- 3,622