All Questions
Tagged with cartesian-closed-categories higher-category-theory
6
questions
10
votes
1
answer
209
views
Weak colimits in locally cartesian closed categories
The general adjoint functor theorem implies that a complete locally small category has a weak colimit of a diagram if and only if it has a colimit of this diagram. It seems that this is also true for ...
- 4,340
3
votes
0
answers
124
views
Is there a construction capturing indexed families of adjunctions?
I'm sorry in advance if this question does not belong on this site. I am curious as to what is "really" going on when you have a family of functors indexed by elements in a base category, all of which ...
- 703
2
votes
1
answer
113
views
When is the derived category $D(A)$ locally cartesian closed?
Let $D(A)$ be the derived $(\infty,1)$-category of some abelian category $A$. For which $A$ is $D(A)$ locally cartesian closed?
Replace $D$ with $D^b$ or similar if appropriate.
I essentially want ...
2
votes
1
answer
326
views
Are lax functor categories into a cartesian closed 2-category cartesian closed?
Suppose that $C$ is a complete closed monoidal category and $I$ is any small category. Then the functor category $Fun(I,C)$ is again a closed monoidal category with the pointwise tensor product $F \...
- 26.9k
1
vote
0
answers
118
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Existence and explicit descriptions for left and right Kan extensions and lifts in bicategories of spans
Given a category $\mathcal{C}$, it follows from Proposition 4.1 of Day's
Brian Day, Limit spaces and closed span categories, Lecture Notes in Mathematics, 420, 1974 (doi:10.1007/BFb0063100).
That ...
1
vote
0
answers
60
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Second order lambda calculus as dinatural transformations in some category of CCCs
Let $\textbf{CART}$ be a category where the objects are all Cartesian closed categories (henceforth shortened as CCC). Is there any way to define the arrows so that $\textbf{CART}$ itself becomes ...
