Display archives based in post_format

No, you cannot define your own post formats. This is on purpose. The post formats are supposed to be standards, so theme developers can include styles for them. That wouldn’t work if people start making their own formats.

Essentially post formats are just a custom taxonomy added to posts. So testing for post format archive pages follow that route. Like this: is_tax ('post_format', 'post-format-aside')

If you want more flexibility you could define your own custom taxonomy. You could even call it ‘post formats’ if you want to.

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