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Results tagged with ct.category-theory
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user 483446
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
10
votes
1
answer
575
views
Universal property of the set of injections in the category of sets
Given two sets $A$ and $B$, the function set $B^A$ is characterized by the universal property that the functor $(-)^A:\mathrm{Set} \to \mathrm{Set}$ is the right adjoint of the functor $(-)\times A:\m …
- 2,624
4
votes
1
answer
434
views
$(n,1)$-dagger categories
In category theory, a dagger category is a precategory $\mathcal{C}$ such that for every pair of objects $A:\mathcal{C}$ and $B:\mathcal{C}$ there is a function $(-)^{\dagger_{A,B}}:\mathrm{Mor}(A,B) …
- 2,624
9
votes
3
answers
1k
views
Axioms for the category of groups
Certain categories of mathematical structures have had synthetic axiom systems developed for them. One particularly well known such category is the category of sets and functions $\mathit{Set}$, which …
- 2,624
0
votes
Sequential colimit of iterated quotients of Cauchy sequences
$\mathrm{QuotCauchy}$ defined above is an endofunctor on the category of Archimedean ordered fields. Thus, the question above is tantamount to asking whether the sequential limit $\mathrm{QuotCauchy}^ …
- 2,624
8
votes
1
answer
231
views
Sequential colimit of iterated quotients of Cauchy sequences
We work in constructive mathematics.
The sets and functions in the foundations form a Grothendieck topos, which means that all colimits exist, and in particular, that all sequential colimits exist. Gi …
- 2,624