Dear All, I hope and pray you and your families are all well. If I may, in the spirit of Merry Christmas lectures, I have a Happy Holidays question (saving my Merry Christmas question for later :-) We can readily think about particulars and generals. In thinking of, say, 0 + 0 = 0, I can readily think of it as a particular of a general: a + a = a. However, doctrine (as a theory of theories, notwithstanding the fact that I can readily think of, say, the SUM doctrine in terms of sum-preserving models of a theory (obtained as a model of the sum doctrine)) doesn't readily lends itself to everyday thinking. There seems to be a dual difficult in perception: I can readily think of the cat I am seeing (sitting on the wall across my window; on a tangential note, I find it little belittling that the cat never looks at me) as a view from a viewshape (i.e. my self-space-time perspective). But, concept (as an abstraction, notwithstanding the fact that I can readily think of, say, the concept CAT as an average of all the cats I saw) doesn't readily lend itself to everyday experience. In aligning the above two difficulties: Doctrine : General : Particular :: Viewshape : Concept : Percept I cannot help but wonder if the algebraic understanding of generals (Professor Andree Ehresmann's sketches, Professor F. William Lawvere's functorial semantics, and late Professor Grothendieck's descent) can be brought to bear on (geometric) concepts, while bringing the geometric understanding of viewshape to inform (algebraic) doctrines. I have to admit that, unlike the correspondence General : Particular :: Concept : Percept it is not clear to me if it is correct to compare (geometric) viewshape with (algebraic) doctrine. I eagerly look forward to your corrections and suggestions! Happy Holidays :-) Thanking you, posina P.S. The correspondence: General : Particular :: Concept : Percept is also problematic; the proper correspondence is: Abstract general (theory) : Concrete General (model) :: Concept : Percept. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]