• 検索結果がありません。

Let (C, J) and (C0, J0) be two sites and let (v, u

N/A
N/A
Info
ダウンロード
Protected

Academic year: 2021

シェア "Let (C, J) and (C0, J0) be two sites and let (v, u"

Copied!
1
0
0

読み込み中.... (全文を見る)

今ダウンロードする ( 1 ページ )

全文

(1)

Problems for Recitation 2

1. LetCbe a category and let (Fi)i∈I be a family of presheaves onC. For every object X ofC, define J(X) to be the set of sievesS onX with the property that for everyi∈Iand every morphism f: Y →X in C, the canonical map

Fi(Y) //limf∗(S)op(Fi)Y,f∗(S)

is a bijection. Show thatJ is a topology onC.

(If the family in question is the family (h(X))X∈ob(C)of all representable presheaves onC, then the topology J is called thecanonical topology.)

2. Let (C, J) and (C0, J0) be two sites and let (v, u, , η) be an adjunction fromC0 toC. Show thatuis continuous if and only ifvis cocontinuous. In this case, show that the functorsusandv∗, or equivalently, the functorsusandv∗ are canonically naturally isomorphic. Conclude that the functoruspreserves finite limits.

1

参照

今ダウンロードする ( PDF - 1 ページ - 112.40 KB )

関連したドキュメント

3. Transnite sites and topoi

Let Si be the 2 -category in the sense of [11, XII.3] whose objects are admissible sites C (Denition 3.6), whose 1 -morphisms are continuous functors C → D preserving nite limits

1, and ∂ν∂ is the outer normal derivative

The study of the eigenvalue problem when the nonlinear term is placed in the equation, that is when one considers a quasilinear problem of the form −∆ p u = λ|u| p−2 u with

(1)NON–ARCHIMEDEAN SEQUENTIAL SPACES AND THE FINEST LOCALLY CONVEX TOPOLOGY WITH THE SAME COMPACTOID SETS A

If τ is the weak topology of ` ∞ and if the field is non-spherically complete, it is shown that τ s coincides with the finest locally convex topology which agrees with τ on norm

A NOTE ON FREE REGULAR AND EXACT COMPLETIONS AND THEIR INFINITARY GENERALIZATIONS

Let C be a co-accessible category with weak limits, then the objects of the free 1 -exact completion of C are exactly the weakly representable functors from C

New York Journal of Mathematics New York J. Math.

of absolute CR -epic spaces: a Tychonoff space X is absolute CR -epic if for any dense embedding X  // Y into another Tychonoff space, the induced C(Y ) // C(X) is an epimorphism in

New York Journal of Mathematics New York J. Math.

If C is a stable model category, then the action of the stable ho- motopy category on Ho(C) passes to an action of the E -local stable homotopy category if and only if the

The Canonical Class and the C

The proof uses a set up of Seiberg Witten theory that replaces generic metrics by the construction of a localised Euler class of an infinite dimensional bundle with a Fredholm

Martin’s Axiom and ω -resolvability of Baire spaces

If there is an almost resolvable space X which is almost-ω- irresolvable, then there is a resolvable Baire open subspace U of X which is hereditarily almost-ω-irresolvable.. Proof: