Discussion of article "Category Theory in MQL5 (Part 2)"
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New article Category Theory in MQL5 (Part 2) has been published:
Category Theory is a diverse and expanding branch of Mathematics which as of yet is relatively uncovered in the MQL5 community. These series of articles look to introduce and examine some of its concepts with the overall goal of establishing an open library that attracts comments and discussion while hopefully furthering the use of this remarkable field in Traders' strategy development.
Isomorphism is a crucial property of homomorphisms in category theory because it ensures that the structure of the domains in the target category is preserved under the mapping. It also guarantees the preservation of the algebraic operations of the domains in the source category. For instance, let's consider a clothing category where the domains are shirts and pants, and the morphisms are the functions that map the size of a shirt to the size of a pant. A homomorphism in this category would be a function that preserves the pairing of the sizes of the shirts to respective sizes of pants. An isomorphism in this category would be a function that not only preserves the algebraic pairing of the sizes, but also establishes a one-to-one correspondence between the sizes of the shirts and pants. This means that for any shirt size, there is exactly one corresponding pant size, and vice versa. For instance, consider the function that maps the size of a shirt (e.g. "small", "medium", "large") to the size of a pant (e.g. "26", "28", "30", "32"). This function is a homomorphism because it preserves and defines a pairing of the sizes (e.g. "small" can be paired with "26" ). But it's not an isomorphism because it doesn't establish a one-to-one correspondence between the sizes of the shirts and pants given that "small" can also be worn with "28" or "26". There is no reversibility.
Author: Stephen Njuki