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16h
revised Explain “homotopy” to me
Fixed grammar
16h
comment Explain “homotopy” to me
Feel free to ask if you need additional clarifications.
16h
answered Explain “homotopy” to me
Feb
7
comment Can we define structures like groups or monoids in the context of pure category theory?
@JoshChen did you mean the commutative version?
Feb
7
revised Can we define structures like groups or monoids in the context of pure category theory?
Added remarks
Feb
7
answered Can we define structures like groups or monoids in the context of pure category theory?
Feb
5
comment Name for categories with a certain property on coproducts
@ZhenLin if that's the case, well, it seems really hard to me that there are any interesting examples where the induced mappings between the hom-sets $\hom(Y,\bigoplus_{i \in I} X_i)$ and $\prod_{i \in I}\hom(Y,X_i)$ are injective.......
Feb
5
comment Name for categories with a certain property on coproducts
What are the projections maps? In a generic category with coproducts there is no reason why you should have natural mappings from $\bigoplus_{i \in I} X_i \to X_i$. Or am I missing something?
Feb
2
comment Type theoretic proof that $\lnot (A \lor B) \Rightarrow \lnot A \land \lnot B$
Well in my opinion in this case one can use chat in an asynchronous way, it isn't really important to have an instant answer.
Feb
1
comment Type theoretic proof that $\lnot (A \lor B) \Rightarrow \lnot A \land \lnot B$
By the way if you want to discuss this arguements I would be very interested, since I'm studying this subject too. Maybe via chat?! ;)
Feb
1
comment Type theoretic proof that $\lnot (A \lor B) \Rightarrow \lnot A \land \lnot B$
Indeed, I supposed so.
Feb
1
answered Type theoretic proof that $\lnot (A \lor B) \Rightarrow \lnot A \land \lnot B$
Feb
1
comment Example of Spherical Element (Simplicial Homotopy)
AAAAAAAH Sorry I forgot you have degeracy maps in $\Delta$, so stupid by me. Again apologize for the confusion.
Feb
1
comment Example of Spherical Element (Simplicial Homotopy)
@NajibIdrissi is the simplicial set with only one $0$-simplex and no simplex in higher dimension. Clearly this cannot be a the terminal simplicial set.
Feb
1
comment Example of Spherical Element (Simplicial Homotopy)
@NajibIdrissi if you like you could think them as two different kind of slice-categories one is the canonical $1/\mathbf{sSet}$, where $1$ is the terminal presheaf, the other one is $S^{0}/\mathbf{sSet}$, where $S^{0}$ represent the simplicial set where $S^{0}_0$ is a singleton and each $S^0_n$ is empty for $n > 0$.
Feb
1
comment Example of Spherical Element (Simplicial Homotopy)
I see, let me be more clear about my doubt. The problem lies in the notion of point you want to use: by point do you mean an element of $X_0$ (that is a $0$-simplex) or a morphism from $1$ (the terminal simplicial set) into $X$?
Feb
1
comment Example of Spherical Element (Simplicial Homotopy)
Could you point out your definition of pointed simplicial set? There are at least two that come to my mind.
Feb
1
comment Prove that a group G is finitely generated if and only if there is a surjective homomorphism $F(\{1,..,n \}) \to G$
@Jxt921 Ok. I wanted to give an hint.... but unfortunately I couldn't find any so I provided a solution. The point is that it seems quite straightforward once you know the properties of homomorphisms and the concrete characterization of free groups......
Feb
1
answered Prove that a group G is finitely generated if and only if there is a surjective homomorphism $F(\{1,..,n \}) \to G$
Feb
1
comment Prove that a group G is finitely generated if and only if there is a surjective homomorphism $F(\{1,..,n \}) \to G$
I don't understand, are you looking for a solution to your problem or do you want an hint?