Giorgio Mossa
Reputation
8,981
Top tag
Next privilege 10,000 Rep.
Access moderator tools
 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.