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Results tagged with cartesian-closed-categories
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user 152679
7
votes
2
answers
642
views
Existence of nontrivial categories in which every object is atomic
An object $X$ of a cartesian closed category $\mathbf C$ is atomic if $({-})^X \colon \mathbf C \to \mathbf C$ has a right adjoint (hence is also internally tiny). Intuitively, atomic objects are "ver …
- 10.7k
8
votes
2
answers
303
views
When is a locally presentable category (locally) cartesian-closed?
Let $\kappa$ be a regular cardinal. A category $\mathscr C$ is locally $\kappa$-presentable iff it is the free completion of a small $\kappa$-cocomplete category under $\kappa$-filtered colimits. Is t …
- 10.7k
2
votes
About cartesian closed categories of models of a cartesian theory
I'll answer the question for algebraic theories, or Lawvere theories, which is the context in which "commutative theories" are typically discussed. This question is then the topic of Johnstone's Colla …
- 10.7k