# Category Theory

## New submissions

[ total of 3 entries: 1-3 ]
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### New submissions for Tue, 20 Mar 18

[1]
Title: Graphs, Ultrafilters and Colourability
Authors: Felix Dilke
Subjects: Category Theory (math.CT); Combinatorics (math.CO)

Let $\beta$ be the functor from Set to CHaus which maps each discrete set X to its Stone-Cech compactification, the set $\beta$ X of ultrafilters on X. Every graph G with vertex set V naturally gives rise to a graph $\beta G$ on the set $\beta V$ of ultrafilters on V . In what follows, we interrelate the properties of G and $\beta G$. Perhaps the most striking result is that G can be finitely coloured iff $\beta G$ has no loops.

[2]
Title: Limits in dagger categories
Subjects: Category Theory (math.CT)

We develop a notion of limit for dagger categories, that we show is suitable in the following ways: it subsumes special cases known from the literature; dagger limits are unique up to unitary isomorphism; a wide class of dagger limits can be built from a small selection of them; dagger limits of a fixed shape can be phrased as dagger adjoints to a diagonal functor; dagger limits can be built from ordinary limits in the presence of polar decomposition; dagger limits commute with dagger colimits in many cases.

### Cross-lists for Tue, 20 Mar 18

[3]  arXiv:1803.06817 (cross-list from math.QA) [pdf, ps, other]
Title: Annular Representations of Free Product Categories