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Results tagged with ct.category-theory
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user 39521
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
1
vote
1
answer
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Natural bijection between sets with coloured elements?
In Andreas Blass's famous paper `Seven Trees in One', the existence of a natural bijection between binary trees and 7-tuples of binary trees is related to the equation $T^7 = T$ being satisfied by a c …
- 12.4k
7
votes
When were triples called monads for the first time?
P. T. Johnstone (who wrote several books on Topos Theory) gave a Category Theory lecture in which he said this was originally called 'the standard construction', then 'triples', and finally 'monads' - …
- 12.4k
40
votes
2
answers
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Ultrafilters as a double dual
Given a set $X$, let $\beta X$ denote the set of ultrafilters. The following theorems are known:
$X$ canonically embeds into $\beta X$ (by taking principal ultrafilters);
If $X$ is finite, then ther …
- 12.4k
15
votes
What is an explicit bijection in combinatorics?
Here's an example (credit: Paul Russell) of the sort of bijection you want to rule out.
Question: Find an explicit bijection $f$ between the size-$k$ and size-$(k + 1)$ subsets of $\{1, 2, \dots, 2k+ …
- 12.4k