A few things to check:
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Did you publish the posts publicly? If you’re publishing in one browser and viewing in another, and you publish a post as a “draft” or “private,” then you won’t be able to see the post in the other browser.
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Are you cached? Try viewing in another browser, and also empty any server-side caches that may be on (check in your plugins and with your web host – sometimes there’s a plugin screen where you need to dump the site cache; other times the hosting CPanel has a cache flush option).
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Switch to a default WP theme, like Twenty Seventeen, and see if you still have the issue. If there’s no issue in the default theme, then you’ll need to check your theme files. If there’s also an issue in the default theme, there may be a problem with your permalinks – go to Settings > Permalinks and see what they are set to for categories. Perhaps the URLs you’re using aren’t the right URLs to access the categories.
Once you’ve checked these, post back and hopefully we can get you further down the troubleshooting path.