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Aug
23
comment Semidirect products with braid groups and type $F_\infty$
Nice trick! Why don't you post it as a regular answer so that I can upvote and accept it? Question too easy?
Aug
22
revised Semidirect products with braid groups and type $F_\infty$
deleted 34 characters in body
Aug
22
comment Semidirect products with braid groups and type $F_\infty$
By permutation of the factors via the projection $B_k\rightarrow S_k$.
Aug
22
asked Semidirect products with braid groups and type $F_\infty$
Aug
20
comment Directed subposet of a poset containing the minimal elements
Thanks Paul for the keywords, I will have to look them up. I used the definition of E in the context of arxiv.org/abs/1407.5171 Definition 6.3. But I have the feeling that there is more behind that definition and that's why I'm asking.
Aug
17
revised Directed subposet of a poset containing the minimal elements
added 60 characters in body
Aug
17
revised Directed subposet of a poset containing the minimal elements
added 115 characters in body
Aug
17
comment Directed subposet of a poset containing the minimal elements
Andreas, yes, there might be no minimal elements in $\{z:x<z>y\}$ and this set even might be empty. However, in my application, there is always at least one minimal element in that set.
Aug
17
asked Directed subposet of a poset containing the minimal elements
Jul
2
awarded  Curious
May
2
accepted Isomorphisms and higher homotopy
May
2
asked Isomorphisms and higher homotopy
May
1
accepted When are automorphisms in categories homotopically trivial?
May
1
comment When are automorphisms in categories homotopically trivial?
Ah, $\gamma$ is still absorbed by $\theta$ (and therefore by $\phi$). Thanks for the example. Btw, the order of the arrows was better before your edit. Path concatenation usually is written from left to right. I always prefer to write $ab$ instead of $b\circ a$ in private so that I don't get confused all day. ;)
May
1
comment When are automorphisms in categories homotopically trivial?
Thanks for the answer. Could you tell me why $\delta$ is null-homotopic? Maybe I'm just blind.
May
1
asked When are automorphisms in categories homotopically trivial?
Mar
30
accepted Reducing the simplices in the nerve of a category with an object with trivial endomorphism monoid
Mar
25
comment Reducing the simplices in the nerve of a category with an object with trivial endomorphism monoid
Could you give me a reference for this?
Mar
24
comment Reducing the simplices in the nerve of a category with an object with trivial endomorphism monoid
As pointed out by მამუკაჯიბლაძე, the arrow $b\rightarrow f$ closes the circle in the full subcategory where $a$ is not present, it is also a $S^1$.
Mar
24
accepted Pushout of categories along embeddings gives homotopy pushout?