## ag.algebraic geometry – About "strict" short exact sequences in quasi-abelian subcategory of a derived category

I read Bridgelands Stability conditions on K3 surfaces, in the Lemma 4.4 a complete quasi-abelian subcategory appears $$mathscr {A} subset mathscr {D}$$ a triangulated category $$mathscr {D} = mathscr {D} (X)$$ of a smooth sort $$X$$, Then he considers a "strict" short exact order
$$0 to A to B to C to 0 tag { * }$$
With $$A, B, C in mathscr {A}$$,

1 question: How exactly do you define (short) exact consequences in a quasi-abelian category?

The definition of abelian categories $$operatorname {Ker} (f_i) = operatorname {im} (f_ {i + 1})$$ seems problematic because I do not know how to define the picture. In general it seems like that $$operatorname {ker coker} f neq operatorname {ker coker} f$$see Wikipedia.

2nd question: What does "strict" mean in this context? Does it have anything to do with the first question, or does it just mean that? $$A neq 0, B neq 0$$these are non-trivial sub-objects / quotients?

Then he argues further $$f (B) = f (A) + f (C)$$, from where $$f: K ( mathscr {D}) to mathbb {R}$$ is an additive function.

3rd question: Why does a short exact sequence $$(*)$$ in the $$mathscr {A}$$ induce a triangle in $$mathscr {D}$$?

I know that this is true, though $$mathscr {A}$$ is Abelian and $$mathscr {D} = mathscr {D} ( mathscr {A})$$ is the derived category of $$mathscr {A}$$but I see no reason why this is true.

Posted on Categories Articles

## How do I create a Child Category page from scratch on WordPress?

As we know, we can create a parent category page directly with the filename category-category_name.php. Is there such a process to create a page for a child category page? That I have
"Continent" – Parent category and
"Country" – Subcategory – I want to create a site with land.

Posted on Categories Articles

## Category theory – Functor with right quasi inverse

But avoid

• Make statements based on opinions; Cover them with references or personal experience.

Use MathJax to format equations. Mathjax reference.

Posted on Categories Articles

## php – Apply category retroactively to posts where the page title matches Regex

I have a bunch of posts that I have to add a category to (too many to handle mass actions, and I do not want to miss any, because admin searching for WP posts is so easy …).

They all follow a predictable title structure for posts (mapping via regex would be easy).

Basically, If the post title matches Regex, apply that category to it,

I found this in WP documents, but it seems too complex for what I need:

function wp_set_post_categories( $post_ID = 0,$post_categories = array(), $append = false ) {$post_ID     = (int) $post_ID;$post_type   = get_post_type( $post_ID );$post_status = get_post_status( $post_ID ); // If$post_categories isn't already an array, make it one:
$post_categories = (array)$post_categories;
if ( empty( $post_categories ) ) { if ( 'post' ==$post_type && 'auto-draft' != $post_status ) {$post_categories = array( get_option( 'default_category' ) );
$append = false; } else {$post_categories = array();
}
} elseif ( 1 == count( $post_categories ) && '' == reset($post_categories ) ) {
return true;
}

return wp_set_post_terms( $post_ID,$post_categories, 'category', $append ); }  Besides, it is not commented, so I have trouble reading it. Posted on Categories Articles ## Category Link go to 404 on store switch I've used Magneto 2 with Store View 2 and My Default Store is English and set Category Link in the Mega Menu, but if I change my store view from English to French, this category link goes to page 404. As the category also shows in the menu. ## ct.category theory – Is a coslice (slice under) category a complete subcategory of the environment category? To let $$operatorname {C}$$ to be a category and $$c in operatorname {C}$$ an object. Consider the category Coslice (sometimes called Slice) $$operatorname {c / C}$$, My question is whether $$operatorname {c / C}$$ is generally a $$textit {full}$$ Subcategory of $$operatorname {C}$$? I am particularly interested in the topic commutative $$operatorname {R-algebras}$$ as a slice category $$operatorname {R / CRing}$$ and thus whether the category $$operatorname {R-Alg}$$ from commutative $$operatorname {R-algebras}$$ a complete subcategory of $$operatorname {CRing}$$, the category of commutative rings. Posted on Categories Articles ## A category can not be deleted in WordPress I can not delete the Gallon Tanks category from my website, and I have no idea why. On my website, the Gallon Tanks category in the navigation menu is not used at all.  ## magento2 – How to create in Magento 2.3.3 not only global, but also in category attributes saved business views? How can I set custom category attributes not only globally but also stored in Magento 2.3.3 in different business views? change & # 39; globally & # 39; => 1 to & # 39; globally & # 39; => 0 seems to make no difference. use MagentoFrameworkSetupInstallDataInterface; use MagentoFrameworkSetupModuleContextInterface; use MagentoFrameworkSetupModuleDataSetupInterface; use MagentoEavSetupEavSetupFactory; class InstallData implements InstallDataInterface { private$eavSetupFactory;

/**
* Constructor
*
* @param MagentoEavSetupEavSetupFactory $eavSetupFactory */ public function __construct(EavSetupFactory$eavSetupFactory)
{
$this->eavSetupFactory =$eavSetupFactory;
}

/**
* {@inheritdoc}
*/
public function install(
ModuleDataSetupInterface $setup, ModuleContextInterface$context
) {
$eavSetup =$this->eavSetupFactory->create(('setup' => $setup));$eavSetup->addAttribute(
MagentoCatalogModelCategory::ENTITY,
'custom_category_field',
(
'type' => 'varchar',
'label' => 'Category Custom field',
'input' => 'text',
'sort_order' => 100,
'source' => '',
'global' => 1,
'visible' => true,
'required' => false,
'user_defined' => false,
'default' => null,
'group' => 'General Information',
'backend' => ''
)
);
}
}


Posted on Categories Articles

## 8 – Drag and drop between the category functions for users

I have a content type where the user selects a specific state and sorts the data for each state based on views. I'd like to create a drop-and-drop feature that allows users to move the box for any content between the states I've seen in Trello. As in the attached screenshot, where I can move a box between application and job interview. So my question is, is there a module for that? If not, what would be the best way to build it? ]

## To change the URL of the WordPress category list

Hello, I would like to change this URL:

https://www.websitename.com/cat/scottish-fold/page/2/

At:

https://www.websitename.com/cat/scottish-fold?page=2

How does it work
I want to do that for seo.

For example:
https://www.searchenginejournal.com/seo-friendly-pagination/275557/