Changes

===Commentary Note 11.13===

===Commentary Note 11.13===

As we make our way toward the foothills of Peirce's 1870 LOR, there is one piece of equipment that we dare not leave the plains without — for there is little hope that "l'or dans les montagnes là" will lie among our prospects without the ready use of its leverage and lifts — and that is a facility with the utilities that are variously called "arrows", "morphisms", "homomorphisms", "structure-preserving maps", and several other names, in accord with the altitude of abstraction at which one happens to be working, at the given moment in question.

As we make our way toward the foothills of Peirce's 1870 LOR, there are several pieces of equipment that we must not leave the plains without, namely, the utilities that are variously referred to as ''arrows'', ''morphisms'', ''homomorphisms'', ''structure-preserving maps'', and several other names, depending on the altitude of abstraction that one happens to be traversing at the moment in question. As a moderate to middling but not too beaten track, I will lay out the definition of a morphism in a number of the forms that we will need right away.

 

As a middle but not too beaten track, I will lay out the definition of a morphism in the forms that we will need right off, in a slight excess of formality at first, but quickly bringing the bird home to roost on more familiar perches.

Let's say that we have three functions ''J'', ''K'', ''L'' that have the following types and that satisfy the equation that follows:

Let's say that we have three functions ''J'', ''K'', ''L'' that have the following types and that satisfy the equation that follows: