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下記の Lawvere Ph.D. thesis は、一読の価値あるな
”The authors comments are F. William Lawvere, 2004.”の部分だけでも、読んでおく価値がある！（＾＾
http://www.tac.mta.ca/tac/reprints/articles/5/tr5abs.html
Functorial Semantics of Algebraic Theories and Some Algebraic Problems in the context of Functorial Semantics of Algebraic Theories
F. William Lawvere
Originally published as:
Ph.D. thesis, Columbia University, 1963
and
in Reports of the Midwest Category Seminar II, 1968, 41-61,
The authors comments are F. William Lawvere, 2004.
http://www.tac.mta.ca/tac/reprints/articles/5/tr5.pdf

https://en.wikipedia.org/wiki/Universal_algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study.
History
Starting with William Lawvere's thesis in 1963, techniques from category theory have become important in universal algebra.[9]
Footnotes
9 Lawvere, William F. (1964), Functorial Semantics of Algebraic Theories (PhD Thesis)

https://en.wikipedia.org/wiki/Category_theory
Category theory
Historical notes
Main article: Timeline of category theory and related mathematics https://en.wikipedia.org/wiki/Timeline_of_category_theory_and_related_mathematics
Category theory may be viewed as an extension of universal algebra, as the latter studies algebraic structures, and the former applies to any kind of mathematical structure and studies also the relationships between structures of different nature.