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.

Category theory – Functor with right quasi inverse

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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.

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.

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' => ''
            )
        );
    }
}

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?

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