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Jan
27
revised If $F : \mathbf{C} \to \mathbf{D}$ is an equivalence, does $\alpha_{GD} = G(\beta_D)$ hold in general?
Make a correction
Jan
27
answered If $F : \mathbf{C} \to \mathbf{D}$ is an equivalence, does $\alpha_{GD} = G(\beta_D)$ hold in general?
Jan
26
answered How do you prove that $Y^*(1_B) = 1_{Y^*B}$ given $Y^*(f) = \mathcal{A}(f, -)$?
Jan
24
answered Homotopy equivalent but not deformation retraction
Jan
24
revised Homotopy equivalent but not deformation retraction
corrected a typo
Jan
24
comment Is the axiom $g1 = g$ essential for a group action
Just a remark: how would you conclude that $(\omega\cdot g)\cdot g^{-1}=\omega$? Usually to prove that one uses the axiom $\omega \cdot 1=\omega$.....
Jan
24
answered Categorical introduction to Algebra and Topology
Jan
23
answered Homotopy colimit,weighted colimit, homotopy theory
Jan
23
comment Isomorphism between categories and how to prove non-isomorphism
I see so basically is the generalization of the composition of two anti-monotone maps.... to be fair I was expecting that but I wanted to be sure, thanks. :)
Jan
23
comment Isomorphism between categories and how to prove non-isomorphism
Just a question: if there is a category whose morphisms include contravariant functors how do you compose two contravariant functors between them? More in details: if you have $F \colon C \to D$ and $G \colon D \to E$ are two contravariant functors (so $F: \colon C^\text{op} \to D$ and $G \colon D^\text{op} \to E$) what is $G \circ F$?
Jan
16
answered Multilinear and alternating property of $\det(f)$ where $f$ is an endomorphism
Jan
11
comment Slice of opposite category equivalent to coslice of category?
@Tim your welcome :)
Jan
11
revised Slice of opposite category equivalent to coslice of category?
changed the direction of the arrows
Jan
11
answered Slice of opposite category equivalent to coslice of category?
Jan
11
revised codiagonal functor and faithfullness
Added a remark
Jan
11
comment codiagonal functor and faithfullness
@nicolas maybe he is me that didn't understood your construction, but you said that objects of $C+C$ should be things like $a+b$ where both $a$ and $b$ are objects of $C$, now in my construction such thing don't exists: elements are either elements of the form $(0,x)$ [or if you like $\text{left} x$] or $(1,x)$ [a.k.a. $\text{right} x$].
Jan
10
comment codiagonal functor and faithfullness
By the way if you prefer I could edit the answer above and use the left and right constructors :)
Jan
10
comment codiagonal functor and faithfullness
@nicolas yes I know that left and right are the ordinary constructors for the sum type, but since on your profile you didn't give any hint on how much type theory do you know I've opted for some standard notation for coproducts (in $\mathbf {Set}$).
Jan
10
answered codiagonal functor and faithfullness
Jan
10
comment codiagonal functor and faithfullness
Ok, so you meant the coproduct.