Is the concept of a "system of times" possible in mathematics?

Bourbaki's formulation: " The essence of mathematics ... is now presented as a study of relations between objects, about which nothing is known, except for some of the properties describing them, namely those that are taken as axioms in the basis of the theory ... Mathematics is a set of abstract forms - mathematical structures. "



A question for those who are related to mathematics:



Is it possible in mathematics, as in a strict, abstract, systematic, linguistic structure, the concept of a" system of times "? And how could she express herself.



If, in ordinary human language, the system of times took shape almost immediately, this, in essence, distinguishes language from the system of animal communication (SCS):

1. "Index marks" (traces) made it possible to pull out the concept (the animal that left traces) from the "here and now" situation, i.e. the animal "once was here", perhaps "will be here", but now it is "somewhere there." This was the first step into the "concept of time".
2. "Iconic signs" (schematic images) allowed the proto-people themselves to create a "concept sign" of the animal, if necessary. This was the second step, increasing the capabilities of the proto-language, allowing signs to move in space, but not yet in time.
3. “Symbols” (abstraction) made it possible to bind the concept to arbitrary signs, a set of signs, create speech syntax and, in fact, create a system of tenses. The sign could not only be moved in space, but also in time using grammar, syntax, etc.

Moreover, in the mathematical language we already have an abstraction, but we do not have a "system of times", a temporal "syntax" of these abstractions. Maybe I don't know something about mathematics (most likely), maybe there is a concept, but it is not yet attached to this possibility.







PS This question arose in connection with the discussion of AI ethics .