Category Theory for Computing Science by Michael Barr, Charles Wells

By Michael Barr, Charles Wells

Good shape. infrequent book!!

Best linear books

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

This e-book is meant as an introductory textual content with reference to Lie teams and algebras and their function in quite a few fields of arithmetic and physics. it truly is written by way of and for researchers who're basically analysts or physicists, no longer algebraists or geometers. now not that we have got eschewed the algebraic and geo­ metric advancements.

Dimensional Analysis. Practical Guides in Chemical Engineering

Useful courses in Chemical Engineering are a cluster of brief texts that every presents a concentrated introductory view on a unmarried topic. the total library spans the most themes within the chemical strategy industries that engineering pros require a easy figuring out of. they're 'pocket guides' that the pro engineer can simply hold with them or entry electronically whereas operating.

Linear algebra Problem Book

Can one research linear algebra completely by means of fixing difficulties? Paul Halmos thinks so, and you'll too when you learn this publication. The Linear Algebra challenge e-book is a perfect textual content for a path in linear algebra. It takes the scholar step-by-step from the fundamental axioms of a box in the course of the thought of vector areas, directly to complicated options resembling internal product areas and normality.

Additional info for Category Theory for Computing Science

Sample text

Also, f is a total function and f (n) = nf (n − 1), so that φ(f ) is defined and by definition of φ, φ(f )(n) = nf (n − 1) = f (n), so φ(f ) = f . If also φ(g) = g, then g(0) = 1 and g(n) = φ(g)(n) = ng(n − 1) so by induction g is the factorial function. The following proposition, applied to the poset P of partial functions, warrants the general recursive construction of functions. 10 Proposition Let (S, ≤) be a strict ω-CPO and f : S − → S a continuous function. Then f has a least fixed point, that is an element p ∈ S with the property that f (p) = p and for any q ∈ S, if f (q) = q then p ≤ q.

A small discrete graph is essentially a set; small discrete graphs and sets are usefully regarded as the same thing for most purposes. 6 Definition A graph is finite if the number of nodes and arrows is finite. 7 Example It is often convenient to picture a relation on a set as a graph. 2) ❄ 4 Of course, graphs that arise this way never have more than one arrow with the same source and target. Such graphs are called simple graphs. 5), and so corresponds to a graph in the sense just described. The resulting picture has an arrow from each element x of the domain to f (x) so it is not the graph of the function in the sense used in calculus.

For example, in the category f ; idB = f , but in the language f and f ; idB are different source programs. This is in contrast to the treatment of languages using context free grammars: a context free grammar generates the actual language. 5 Example As a concrete example, we will suppose we have a simple such language with three data types, NAT (natural numbers), BOOLEAN (true or false) and CHAR (characters). We give a description of its operations in categorical style. (i) NAT should have a constant 0 : 1 − → NAT and an operation succ : NAT − → NAT.