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27 changes: 0 additions & 27 deletions content/Meas_not_regular.md

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74 changes: 0 additions & 74 deletions content/aleph1-cofiltered-limits-fg-groups.md

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118 changes: 0 additions & 118 deletions content/aleph1-filtered-colimits-in-deloopings.md

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2 changes: 1 addition & 1 deletion content/contribute.md
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Expand Up @@ -5,7 +5,7 @@ description: CatDat welcomes contributions from the community, including filling

## How to contribute

_CatDat_ is developed in an open-source [GitHub repository](https://github.com/ScriptRaccoon/catdat) owned by [Martin Brandenburg](https://ncatlab.org/nlab/show/Martin+Brandenburg). It welcomes contributions from the community, including filling in missing information or discovering new combinations of properties.
_CatDat_ is developed in an open-source [GitHub repository](https://github.com/ScriptRaccoon/catdat) by [Martin Brandenburg](https://ncatlab.org/nlab/show/Martin+Brandenburg). It welcomes contributions from the community, including filling in missing information or discovering new combinations of properties.

[**Video tutorial**](https://www.youtube.com/watch?v=NoZWdMFfQfg)

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4 changes: 2 additions & 2 deletions content/generator_construction.md
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---
title: Construction of Generators
title: Construction of generators
description: How to construct a generator from a generating set
---

## Construction of Generators
## Construction of generators

::: Lemma
In a category let $S$ be a generating set which is [strongly connected](/category-property/strongly_connected), i.e. between any two objects $G,G' \in S$ there is a morphism $G \to G'$. If the coproduct $U \coloneqq \coprod_{G \in S} G$ exists, then it is a generator. Moreover, if $S$ is an extremal generating set, then $U$ is an extremal generator.
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4 changes: 2 additions & 2 deletions content/resources.md
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---
title: Resources on Category Theory
title: Resources on category theory
description: This is an (incomplete) list of resources on category theory.
---

## Resources on Category Theory
## Resources on category theory

This is an (incomplete) list of resources on category theory.

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4 changes: 2 additions & 2 deletions content/thin_extremal_generator.md
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---
title: Thin Category with an Extremal Generator
title: Extremal generators in thin categories
description: A result restricting which thin categories can have an extremal generator
---

## Thin Category with an Extremal Generator
## Extremal generators in thin categories

::: Lemma
Suppose $G$ is an object of a thin category. Then $G$ is an extremal generator if and only if for every object $X$, either $X \cong G$ or every morphism with codomain $X$ is an isomorphism.
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4 changes: 2 additions & 2 deletions content/topos-with-generator.md
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---
title: Topos with a Generator
title: Topos with a generator
description: An elementary topos with a generator has at most two subterminal objects
---

## Topos with a Generator
## Topos with a generator

::: Lemma
Suppose a category is coregular, and it has disjoint finite coproducts, a terminal object, and a generator. Then every regular subterminal object (i.e. an object $X$ such that the unique morphism $X \to 1$ is a regular monomorphism) is either initial or terminal.
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