Following the seminal paper by H. Petard in 1938 introducing to the mathematical theory of big game hunting, a good many others were prompted to add to this literature. The following is one of these articles.

#### On a theorem of H. Petard

– Christian Roselius

Tulane University

In a classical paper [4], H. Petard proved that it is possible to capture a lion in the Sahara desert. He further showed [4, no. 8, footnote] that it is in fact possible to capture every lion with at most one exception. Using completely new techniques, unavailable to Petard at the time, we are able to sharpen this result, and to show that *every* lion may be captured.

Let *L* denote the category whose objects are lions, with “ancestor” as the only nontrivial morphism. Let *C* be the category of caged lions. The subcategory *C* is clearly complete, is nonempty (by inspection), and has both a generator and cogenerator [3, vii, 15-16]. Let *F* : *C* ® *L* be the forgetful functor, which forgets the cage. By the Adjoint Functor Theorem [1, 80-91] the functor *F* has a coadjoint *G* : *L* ® *C*, which reflects each lion into a cage.

We remark that this method is obviously superior to the Good method [2], which only guarantees the capture of one lion, and which requires an application of the Weierkafig Preparation Theorem.

#### References

[1] P. Freyd, Abelian categories, New Yor, 1964.

[2] I. J. Good, A new method of catching a lion, Amer. Math. Monthly, 72 (1965) 436.

[3] Moses, The Book of Genesis.

[4] H. Petard. A contribution to the mathematical theory of big game hunting, Amer. Math. Monthly 45 (1938) p446-447.

*Amer. Math. Monthly *74 (1967), p. 838-839.