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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.
Jan
10
comment codiagonal functor and faithfullness
It is not clear to me what the category $C + C$ should be. Could you point out the exact reference in Awodey's book? (I assume you are talking of Awodey's Category Theory book).
Jan
10
comment Need a formal proof?
@HumaJamil your argument is perfectly sound :)
Jan
10
answered Need a formal proof?
Jan
8
comment Prove that theory is not Henkin one
By the way... with your defintion it seems that the empty theory is an Henkin theory.
Jan
8
comment Prove that theory is not Henkin one
Mind if I ask what is your reference for the subject?
Jan
7
revised Understanding types and the proof that every type is realized in an elementary extension.
The tag type-theory is innapropriate for the question
Jan
6
answered Natural transformations in Awodey's Category Theory Exercise 7.11.8
Jan
6
comment Natural transformations in Awodey's Category Theory Exercise 7.11.8
Note that it isn't true that $\pi_1^{FD \times GD}\circ F(f)\times G(f)=F(f)$ because the first morphism belongs to $\mathbf D[F(C),F(D)]$ while the second belongs to $\mathbf D[F(C)\times G(C),F(D)]$.
Jan
6
answered $\mathcal{V}$-naturality in enriched category theory
Jan
6
comment What is this categorical notion called?
@JasonEliot I'm not aware if the notion of meet is used in this general sense (intersection up to isomorphism).
Jan
6
comment What is this categorical notion called?
@JasonEliot it stops to work because you don't have Cantor-Berstein in theorem in general categories: that's is it is not necessarily true that if you have to monomorphisms $X \to Y$ and $Y \to X$ then you have an isomorphism between the objects $X$ and $Y$.
Jan
6
revised What is this categorical notion called?
Correct some errors
Jan
6
answered What is this categorical notion called?