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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.
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
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
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