. "1"^^ . . "Representability Relative to a Doctrine" . "RIV/68407700:21230/09:03154635!RIV09-MSM-21230___" . "Z(MSM6840770014)" . "2"^^ . "339008" . . "Karazeris, P." . "multilimit; weighted limit; promonoidal structure"@en . "Zav\u00E1d\u00EDme pojem doktr\u00EDny jako\u017Eto jednotn\u00E9ho prost\u0159ed\u00ED pro studium slab\u00FDch pojm\u016F representability. Proto\u017Ee (ko)limity lze definovat pomoc\u00ED representability, umo\u017E\u0148uje pojem doktr\u00EDny definovat a studovat oslaben\u00E9 (ko)limitn\u00ED pojmy. Pokud je danou doktr\u00EDnou nap\u0159\u00EDklad doktr\u00EDna koz\u00FApln\u011Bn\u00ED na kolimity jist\u00E9 t\u0159\u00EDdy, existence oslaben\u00FDch limit v kategorii ma bl\u00EDzk\u00FD vztah ke skute\u010Dn\u00FDm limit\u00E1m ve voln\u00FDch koz\u00FApln\u011Bn\u00EDch. Analogick\u00FD vztah plat\u00ED mezi promonoid\u00E1ln\u00EDmi strukturami na kategorii a skute\u010Dn\u00FDmi monoid\u00E1ln\u00EDmi strukturami na voln\u00FDch koz\u00FApln\u011Bn\u00EDch."@cs . "Representability Relative to a Doctrine"@en . . . . . "Representabilita vzhledem k doktr\u00EDn\u011B"@cs . . "Representability Relative to a Doctrine" . "Cahiers de topologie et geometrie differentielle categoriques" . . "20"^^ . . "21230" . "XLX-1" . . "Representability Relative to a Doctrine"@en . "Velebil, Ji\u0159\u00ED" . "RIV/68407700:21230/09:03154635" . "We propose the notion of a doctrine to provide a uniform environment for studying weak representability concepts. Since (co)limits are representability notions, this allows us to define and study weakened (co)limit concepts. For example, in case the doctrine in question is the doctrine of free cocompletions under colimits of some class, the existence of weakened limits in the ambient category is closely related to honest limits in free cocompletions. Similarly, we can relate certain weak promonoidal structures on a category to honest monoidal structures on a free cocompletion." . "2009" . . "We propose the notion of a doctrine to provide a uniform environment for studying weak representability concepts. Since (co)limits are representability notions, this allows us to define and study weakened (co)limit concepts. For example, in case the doctrine in question is the doctrine of free cocompletions under colimits of some class, the existence of weakened limits in the ambient category is closely related to honest limits in free cocompletions. Similarly, we can relate certain weak promonoidal structures on a category to honest monoidal structures on a free cocompletion."@en . "[61030C60C823]" . "0008-0004" . "Representabilita vzhledem k doktr\u00EDn\u011B"@cs . "FR - Francouzsk\u00E1 republika" . . . .