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I construct a category, which I call “category of pointfree funcoid triples”, you may find it in my draft book.
Currently in the above mentioned PDF file there are several errors (marked with red-font FIXME) on this topic, however this does not matter.
This category of reloid triples can be extended to a greater precategory “precategory of pointfree funcoid triples” which is not a category.
I present this category in my book just for completeness, I don’t use them later in my research.
My question: Is it worth to care about precategories? I mean: Is it worth to introduce special definition and/or notation for this precategory which has only some, not all identities? Or does missing identities make it uninteresting and not worth mentioning?
See semicategory. They certainly have their uses.
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