Consider a cartesian closed category where the exponential object is $[A \to B] = B^A$. The following kind of isomorphism is stated in my book as evident: $\operatorname{Hom}(1, [\cdot \times B \to C]) \cong \operatorname{Hom}(\cdot \times B, C)$ Here $1$ should be the terminal object of the ca...

It is often said that the category $\sf Top$ of topological spaces and continuous mappings is not cartesian closed. E.g., in the Wikipedia article on compactly generated spaces and in an answer on this site. Can anyone point me at a proof that $\sf Top$ cannot be made into a cartesian closed cate...

In some (but not all) of the published definitions, a locally cartesian closed category is any category with all its slices cartesian closed. Such a category need not be cartesian closed itself, simply because it need not have a terminal object. As a prominent example, there is the $n$-categor...

I'm trying to get started learning category theory. A problem I'm working on is to show that for a set $S$, the partial order $(\mathcal{P}(S),\subseteq)$ viewed as a category is cartesian closed. So far, I was thinking that $S$ is the terminal object, and that the product of any two subsets $...

I am programmer (from the object oriented world) and currently getting my head around functional programming. I was looking to get some basics right. I understand what category theory and lambda calculus try and tell . I did read that lambda calculus can be modelled in any Cartesian closed categ...

support feature-request status-planned According to What tags exist by default on child metas?, there is a default [favorites] tag on all ~170 child metas in the network, e.g. on Meta Stack Overflow but also on the newest private beta site. To give you an idea how often it is used in practice, s...