2d
comment What is the opposite of $\colon\colon$?
What does "not 3:12:4692" mean? Sounds like you chose strange numbers.
Jun
29
accepted Weibel definition 1.4.1. understanding the indexes on splitting maps
Jun
29
accepted Question about an inverse limit.
Jun
29
comment Question about an inverse limit.
@AmitaiYuval I'm not sure what they look like.
Jun
29
asked Question about an inverse limit.
Jun
29
revised Weibel definition 1.4.1. understanding the indexes on splitting maps
added 115 characters in body
Jun
29
asked Weibel definition 1.4.1. understanding the indexes on splitting maps
Jun
29
comment These maps from the components into a directed system are injective when the directed system maps are.
Ah, same mistake I made last time. Forgetting what sets the arguments are in.
Jun
29
accepted These maps from the components into a directed system are injective when the directed system maps are.
Jun
29
asked These maps from the components into a directed system are injective when the directed system maps are.
Jun
28
comment Proving that the direct limit of a directed system is an equivalence relation.
I've got it now. Using the composition condition you can show that $\exists, i,j, \ell \leq k$ (by directedness, you can show both statements under one $k$.) such that $p_{ik}(a) = p_{jk}(b) = p_{\ell k}(c)$ done. Thanks for teaching!
Jun
28
comment Proving that the direct limit of a directed system is an equivalence relation.
In your first statement you made a mistake of re-using the variable $j$, we know that some $j'$ exists but not that it equals $j$
Jun
28
comment Proving that the direct limit of a directed system is an equivalence relation.
I have to ruminate for a second on this at my dry-erase board.
Jun
28
comment Proving that the direct limit of a directed system is an equivalence relation.
I'm having trouble piecing it together. I have $a \sim b \iff \exists i,j \leq k$ with $p_{ik}(a) = p_{jk}(b)$, $b \sim c \iff \exists i',j'\leq k'$ with $p_{i'k'}(b) = p_{j'k'}(c)$ and $\forall i,j \in I \exists k$ with $i,j \leq k$, and $p_{jk} \circ p_{ij} = p_{ik}$ whenever $i \leq j \leq k$. Still thinking on it though.
Jun
28
comment Proving that the direct limit of a directed system is an equivalence relation.
Ah, the book even states this.
Jun
28
accepted Proving that the direct limit of a directed system is an equivalence relation.
Jun
28
asked Proving that the direct limit of a directed system is an equivalence relation.
Jun
27
revised The related concepts to a special statement
added 18 characters in body
Jun
26
comment The related concepts to a special statement
@MattSamuel I don't see what that has to do with anything. $a^{-1}$ isn't an expression of power, it's a convention of writing the inverses by.
Jun
26
answered The related concepts to a special statement
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