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 Yearling
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comment Orthogonal Factorization Systems and functoriality
@Arrow I thin you mixed something up here. $F_0$ is uniquely determined up to isomorphisms and only defined on objects $x\xrightarrow{f} y$ in $\mathcal{C}^{[1]}$. The extension to a functor $F$ is then given by mapping morphisms $(u,v)$ in $\mathcal{C}^{[1]}$ to morphisms $(u,\omega, v)$. I'm not sure right now if this extension is unique, or if you could do something weird like sending all morphisms in $\mathbf{Grp}^{[1]}$ to those mapping everything to the neutral element. But it's at least the unique natural extension. Where uniqueness is guaranteed by (III).
2d
awarded  Yearling
2d
revised Orthogonal Factorization Systems and functoriality
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2d
revised Orthogonal Factorization Systems and functoriality
added 368 characters in body
2d
revised Orthogonal Factorization Systems and functoriality
added 312 characters in body
2d
revised Orthogonal Factorization Systems and functoriality
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answered Orthogonal Factorization Systems and functoriality
2d
comment How old is the distinction of right homotopy from left homotopy?
@Colin McLarty: If you found an answer, I would love to hear it. Leaving this question unanswered is a shame.
Apr
25
comment How do I compute the first few digits of √11 in $\Bbb Q_5$
What have you tried, where are you stuck?
Apr
25
asked CW-complex via composition of pushouts and there characteristic maps
Apr
25
accepted The significance of CW-complexes in homotopy theory
Apr
19
reviewed No Action Needed Question about the solution to the heat equation?
Apr
16
revised Matrix representation of an anticommuting function
fixed math
Apr
16
reviewed Reviewed Matrix representation of an anticommuting function
Apr
16
suggested approved edit on Matrix representation of an anticommuting function
Apr
16
asked The significance of CW-complexes in homotopy theory
Apr
11
comment Difference between simplicial complex and underlying space
In order to draw a picture of a simplicial complex, you need to know the underlying topological space since this is exactly what you're drawing. The simplicial complex itself is just a collection of sets.
Apr
8
comment What is the meaning of the notation $A :\Leftrightarrow B$?
@Saphrosit Maybe you should note that something like: "We define a relation $>$ on $\mathbb{N}$ via $n>m\iff n|m$" is perfectly fine.
Apr
8
comment What is the meaning of the notation $A :\Leftrightarrow B$?
@Yuaxiao $:\iff$ is restricted to statements. If you can read it out loud and answer with "true" or "false", use $:\iff$. Using the first two examples, the first reads "f of x" and the second reads "f of x greater than zero". The second one clearly is answerable, the first one isn't.
Apr
8
awarded  Custodian