In Japanese, English (katakana) words are regularly abbreviated (短縮・省略される), but often in different ways to native English so you need to be careful.
One example is “air-con” (エアコン), which in English would be shortened to AC or A/C. We often abbreviate words by using initialism (頭文字語) like this but using longer parts of the words like in Japanese is much rarer. (NOTE: “cooler” (クーラー) is also Japanese English (和製英語) and means something different in English).
However there are some exceptions (例外) especially in slang (スラング、俗語). For example “rom-com”, which is short for romantic comedy. Another example is “sci-fi”, which is short for science fiction, when in Japanese the initialism SF is usually used.
Abbreviations of longer words and phrases are also common in Japanese, such as「コンビニ」 or 「デパート」, but these would be impossible to understand in native English (both are missing the key word “store”…).
We would always need to say the full word or phrase, i.e. convenience store or department store. Instead of shortening words like this natives may use shorter slang words.
On the other hand, some words in English are shortened in ways that may seem illogical (非論理的な、不合理な) to non-natives. One example is refrigerator which is shotened to “fridge” in English and not refridge (also notice that an extra “d” was added to the shortened word). Another example is influenza which is shortened to “flu” in English and not “influ” (インフル) like in Japanese.
If you want to know how a word is usually abbreviated in English
you can often find the answer in the dictionary or by doing a web search.